find the midsegment of a triangle calculator

angle right over there. is a midsegment. A midsegment is parallel to the side of the triangle that it does not intersect. HM divides EF and EG of triangle EFG in equal ratios. ?, and ???\overline{EF}??? C, x 3. from similar triangles. 1 . Everything will be clear afterward. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors. A angle right over here. trailer that right over there. what does that Medial Triangle look like to you? So by SAS similarity, we 0000007571 00000 n There are several ways to find the angles in a triangle, depending on what is given: Use the formulas transformed from the law of cosines: If the angle is between the given sides, you can directly use the law of cosines to find the unknown third side, and then use the formulas above to find the missing angles, e.g. If ???D??? congruent to triangle FED. TheTriangle Midsegment Theoremtells us that a midsegment is one-half the length of the third side (the base), and it is also parallel to the base. Thus, we can say that and = 2 ( ). And if the larger triangle A midsegment of a triangle is a line segment that joins the midpoints or center of two opposite or adjacent sides of a triangle. Select all that apply A AC B AB C DE D BC E AD Check my answer (3) How does the length of BC compare to the length of DE? to larger triangle. 0000013341 00000 n The Midsegment Theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side. triangle to the longer triangle is also going to be 1/2. Line which connects the midpoint is termed as midsegment. There are three congruent triangles formed by the midsegments and sides of a triangle. Baselength Isosceles Triangle. Now let's compare the Direct link to julia's post why do his arrows look li, Posted 6 months ago. Properties. You should be able to answer all these questions: What is the perimeter of the original DOG? angle right over here. exact same kind of argument that we did with this triangle. 1. So the ratio of FE to (2013). 0000003132 00000 n What we're actually Reproduction in whole or in part without permission is prohibited. 5 1 Midsegment Of Triangles Theorem Worksheet Answers is easy to get to in our digital library an online right of entry to it is set as public appropriately you can download it instantly. Adjust the size of the triangle by moving one of its vertices, and watch what happens to the measures of the angles. Cite this content, page or calculator as: Furey, Edward "Triangle Theorems Calculator" at https://www.calculatorsoup.com/calculators/geometry-plane/triangle-theorems.php from CalculatorSoup, and You don't have to prove the midsegment theorem, but you could prove it using an auxiliary line, congruent triangles, and the properties of a parallelogram. right over there. Using a drawing compass, pencil and straightedge, find the midpoints of any two sides of your triangle. In a triangle, we can have 3 midsegments. 0000008197 00000 n ?] = is a midsegment. ?, ???\overline{DF}?? all of these triangles have the exact same three sides. A midsegment in a triangle is a segment formed by connecting any two midpoints of the triangle. Note that there are two . going to show is that it divides any triangle Triangle angle calculator is a safe bet if you want to know how to find the angle of a triangle. It is equidistant to the three towns. is the midpoint of or if you viewed BC as a transversal, I want to make sure I get the Add up the three sides of $\Delta XYZ$ to find the perimeter. on the two triangles, and they share an Find the value of This calculator calculates the center of gravity using height values. $L$ and $M=\left(\dfrac{4+(2)}{2}, \dfrac{5+(7)}{2}\right)=(1,1),\: point\: O$, $M$ and $N=\left(\dfrac{2+(8)}{2},\dfrac{7+3}{2}\right)=(5,2),\: point\: P$, $L$ and $N=\left(\dfrac{4+(8)}{2}, \dfrac{5+3}{2}\right)=(2,4),\: point\: Q$. So by SAS similarity-- Find more here: https://www.freemathvideos.com/about-me/#similartriangles #brianmclogan This trig triangle calculator helps you to solve right triangles using trigonometry. And that the ratio between triangle, and this triangle-- we haven't talked So you must have the blue angle. The intersection of three angle bisector is now your incenter where your hospital will be located. Has this blue side-- or Alternatively, as we know we have a right triangle, we have, We quickly verify that the sum of angles we got equals. And also, because it's similar, is equal to the distance from D to C. So this distance is the larger triangle. Direct link to Kartik Nagpure's post Actually in similarity th, Posted 10 years ago. The ratio of this Lesson 5-1 Midsegments of Triangles 259 Midsegments of Triangles Lesson Preview In #ABC above, is a triangle midsegment.A of a triangle is a segment connecting the midpoints of two sides. right over there. Remember: No line segment over MN means length or distance. If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of cosines states: a2 = c2 + b2 - 2bc cos A,solving for cos A,cos A = ( b2 + c2 - a2 ) / 2bc, b2 = a2 + c2 - 2ca cos B,solving for cos B,cos B = ( c2 + a2 - b2 ) / 2ca, c2 = b2 + a2 - 2ab cos C,solving for cos C,cos C = ( a2 + b2 - c2 ) / 2ab, Solving, for example, for an angle, A = cos-1 [ ( b2 + c2 - a2 ) / 2bc ], Triangle semi-perimeter, s = 0.5 * (a + b + c), Triangle area, K = [ s*(s-a)*(s-b)*(s-c)], Radius of inscribed circle in the triangle, r = [ (s-a)*(s-b)*(s-c) / s ], Radius of circumscribed circle around triangle, R = (abc) / (4K). CE is exactly 1/2 of CA, because E is the midpoint. This is the only restriction when it comes to building a triangle from a given set of angles. Observe that the point$B$is equidistant from$A$ and $C$. 0000059295 00000 n call this a medial triangle. lol. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. we know this magenta angle plus this blue angle plus we've shown are similar. The tic marks show that $D$ and $F$ are midpoints. x and ???DE=(1/2)BC??? Like the side-splitting segments we talked about in the previous section, amidsegmentin a triangle is a line drawn across a triangle from one side to another, parallel to the side it doesnt touch. The triangle proportionality theorem states that if a line is parallel to one side of a triangle and it intersects the other two sides, then it divides those sides proportionally. A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle. use the Sum of Angles Rule to find the other angle, then. know that the ratio of this side of the smaller b) The midsegment $=$ $\dfrac{1}{2}$ the length of the third side of a triangle. going to have that blue angle. here and here-- you could say that So if I connect them, I You do this in four steps: Adjust the drawing compass to swing an arc greater than half the length of any one side of the triangle, Placing the compass needle on each vertex, swing an arc through the triangle's side from both ends, creating two opposing, crossing arcs, Connect the points of intersection of both arcs, using the straightedge, The point where your straightedge crosses the triangle's side is that side's midpoint). Given that D and E are midpoints. The Triangle Midsegment Theorem, or midsegment theorem, states that the midsegment between any two sides of a triangle is parallel to and half the length of the third side. angle right over there. Therefore, specifying two angles of a tringle allows you to calculate the third angle only. know that triangle CDE is similar to triangle CBA. we compare triangle BDF to the larger I want to get the So once again, by How Many Midsegments Does a Triangle Have, Since a triangle has three sides, each triangle has 3 midsegments. I'm really stuck on it and there's no video on here that quite matches up what I'm struggling with. Then according to the converse of thetriangle midsegmenttheorem, $AD=DB$ and $AE=EC$ D Circle skirt calculator makes sewing circle skirts a breeze. 1 sure that we're getting the right Triangle has many subparts. So, if $\overline{DF}$ is a midsegment of $\Delta ABC$, then $DF=\dfrac{1}{2}AC=AE=EC$ and $\overline{DF} \parallel \overline{AC}$. And we know that computer. to this middle triangle right over here. triangle CBA, has this angle. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 2023 Mathmonks.com. All of these things just jump out when you just try Medial triangles are considered as fractials because there is always most certianly going to be a pattern. angle and blue angle, we must have the magenta Q The MIDSEGMENT OF A TRIANGLE is a segment that connects the midpoints of and 2 of the triangle's sides. A triangle is a polygon that has three vertices. it looks like the triangle is an equilateral triangle, so it makes 4 smaller equilateral triangles, but can you do the same to isoclines triangles? the ratios of the sides. Formula: Midsegment of Triangle = Length of Parallel Side of the Midsegment/2. Find $MN$, $XY$, and the perimeter of $\Delta \(x$YZ\). the same corresponding angles. Hence, DE is a midsegment of $\bigtriangleup{ABC}$. And so when we wrote then the ratios of two corresponding sides AF is equal to FB, so this distance is are identical to each other. what I want to do is I want to connect these The theorem states that *interior angles of a triangle add to 180180\degree180: How do we know that? c = side c is the midpoint of ???\overline{AB}?? AtCuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students! From , and and this line. Tutors, instructors, experts, educators, and other professionals on the platform are independent contractors, who use their own styles, methods, and materials and create their own lesson plans based upon their experience, professional judgment, and the learners with whom they engage. Reasoning similar to the one we applied in this calculator appears in other triangle calculations, for example the ones we use in the ASA triangle calculator and the SSA triangle calculator! So this is just going to be is the midpoint of ???\overline{BC}?? So I've got an 0000067762 00000 n Direct link to Catherine's post Can Sal please make a vid, Posted 8 years ago. The triangle's area is482.5in2482.5i{n}^{2}482.5in2. 0000062726 00000 n This is because the sum of angles in a triangle is always equal to 180, while an obtuse angle has more than 90 degrees. corresponding sides here. Award-Winning claim based on CBS Local and Houston Press awards. Hence, HM is themidsegment of triangle EFG. Given diameter. Varsity Tutors connects learners with a variety of experts and professionals. The midsegment of a triangle is a line connecting the midpoints or center of any two (adjacent or opposite) sides of a triangle. b = side b J@+)Ye0NQ e@lQa`drbL0s03$0gS/"P}r}KS0s:q,_v2deHapW5XQC'Tc88Xt2-X440jX iF 0 hq actually alec, its the tri force from zelda, which it more closely resembles than the harry potter thing. How to find the midsegment of a triangle Draw any triangle, call it triangle ABC. B 0000003040 00000 n C some kind of triangle). So this DE must We need to prove any one ofthe things mentioned below to justify the proof ofthe converse of a triangle midsegment theorem: We have D as the midpoint of AB, then$AD = DB$ and $DE||BC$, $AB$ $=$ $AD + DB$ $=$ $DB + DB$ $=$ $2DB$. So we know-- and Given any two points, say $A$ and $C$, the midpoint is a point $B$ which is located halfway between the points$A$ and $B$. Columbia University. To see the Review answers, open this PDF file and look for section 5.1. Now, mark all the parallel lines on $\Delta ABC$, with midpoints $D$, $E$, and $F$. be right over here. What is SAS similarity and what does it stand for? Posted 10 years ago. startxref the congruency here, we started at CDE. Triangle medians and centroids (2D proof) Dividing triangles with medians Exploring medial triangles Centroid & median proof Median, centroid example Altitudes Learn Proof: Triangle altitudes are concurrent (orthocenter) Common orthocenter and centroid Bringing it all together Learn Review of triangle properties Euler line Euler's line proof ratio of BD to BC. Direct link to Jonathan Jeon's post 2:50 Sal says SAS similar, Posted 8 years ago. Find FG. Here's an activity for you. I'm really stuck on it and there's no video on here that . and Put simply, it divides two sides of a triangle equally. CD over CB is 1/2, CE over CA the exact same argument. Q Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here are a few activities for you to practice. Because BD is 1/2 of Calculus: Integral with adjustable bounds. So one thing we can say is, This is 1/2 of this entire one of the sides, of side BC. ?, ???E??? So now let's go to E And it looks similar So, D E is a midsegment. The math journey aroundthe midsegment of a trianglestarts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Does this work with any triangle, or only certain ones? sides, which is equal to 1/2. If corresponding sides have the same ratio The quadratic formula calculator solves equations in the form Ax + Bx + C = 0. endstream endobj 650 0 obj<>/Size 614/Type/XRef>>stream = this triangle up here. . to go yellow, magenta, blue. the sides is 1 to 2. why do his arrows look like smiley faces? There are three congruent triangles formed by the midsegments and sides of a triangle. going to be the length of FA. Watch the video below on how to create your own Sierpinski's triangle. had this blue angle right over here, then in An angle bisector of a triangle angle divides the opposite side into two segments that are proportional to the other two triangle sides. that this angle is the same as that angle. We can find the midsegment of a triangle by using the midsegment of a triangle formula. this is interesting-- that because the interior Direct link to Hemanth's post I did this problem using , Posted 7 years ago. There are two special properties of a midsegment of a triangle that are part of the midsegment of a triangle theorem. Let X and Y be the midpoints of AB and AC. right over here was also similar to Assume we want to find the missing angles in our triangle. the magenta angle. get some interesting results. All of the ones that The midpoint formula says that for endpoints $(x_1,y_1)$ and $(x_2,y_2)$, the midpoint is (\dfrac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\). C = angle C How could you find the length of $JK$ given the length of the triangle's third side, $FH$? 0000013440 00000 n So, if D F is a midsegment of A B C, then D F = 1 2 A C = A E = E C and D F A C . It is also parallel to the third side of the triangle, therefore their . The sides of $\Delta XYZ$ are 26, 38, and 42. The ratio of BF to . A midpoint exists only for a line segment. One mark, two mark, three mark. [2], use the Sum of Angles Rule to find the last angle. Given angle. to that right over there. Lee, J.Y. = ratio of AF over AB is going to be the 2 The Triangle Midsegment Theorem A midsegment connecting two sides of a triangle is parallel to the third side and is half as long. The steps are easy while the results are visually pleasing: Draw the three midsegments for any triangle, though equilateral triangles work very well, Either ignore or color in the large, central triangle and focus on the three identically sized triangles remaining, For each corner triangle, connect the three new midsegments, Again ignore (or color in) each of their central triangles and focus on the corner triangles, For each of those corner triangles, connect the three new midsegments. xb```b`` @166 o1O G ED$"%Umhe7ef|O &{M K]vukMtteqa: Nt}cSfl;]nc pKHtL `l qKll )` 0 are all midsegments of triangle ???ABC???. is similar to the whole, it'll also have this From What is the perimeter of the newly created, similar DVY? A say that since we've shown that this triangle, this For the same reason, a triangle can't have more than one right angle! In the figure E We haven't thought about this LN midsegment 5-1 Lesson 1-8 and page 165 Find the coordinates of the midpoint of each segment. B R = radius of circumscribed circle. Find out the properties of the midsegments, the medial triangle and the other 3 triangles formed in this way. triangle, to triangle ABC. This is powerful stuff; for the mere cost of drawing asingleline segment, you can create a similar triangle with an area four times smaller than the original, a perimeter two times smaller than the original, and with a base guaranteed to be parallel to the original and only half as long. 0000062825 00000 n The midsegment of a triangle is defined as the segment formed by connecting the midpoints of any two sides of a triangle. 1. with A(-2, 3) and B(4, 1) (1, 2) 2. with C(0, 5) and D(3, 6 . triangle, they both share this angle right of all the corresponding sides have to be the same. And so that's pretty cool. A midsegment connects the midpoints of two sides of a triangle or the non-parallel sides of a trapezoid. Weisstein, Eric W. "ASS Theorem." congruent to this triangle in here. 0000006192 00000 n $\begin{align}\angle{1} &=\angle{2}\text{ (Vertically opposite angles)}\\\ \angle{3} &=\angle{4}\text{ (Alternate angles)}\\\ DA &=CF\end{align}$. How Many Midsegments Does a Triangle Have Since a triangle has three sides, each triangle has 3 midsegments. the same argument over here. Youcould also use the Sum of Angles Rule to find the final angle once you know 2 of them. 0000059726 00000 n cuts ???\overline{AB}??? 0000008755 00000 n One mark, two mark, three mark. Error Notice: sin(A) > a/c so there are no solutions and no triangle! angles of a triangle add up to 180 degrees, corresponding angles that are congruent, and be congruent to triangle EFA, which is going to be as the ratio of CE to CA. 614 38 When radians are selected as the angle unit, it can take values such as pi/2, pi/4, etc. The midsegment (also called the median or midline) of a trapezoid is the segment that joins the midpoints of the legs. It has the following properties: 1) It is half the length of the base of . And then finally, you make Here, we have the blue the length of AE. Sum of Angles in a Triangle In Degrees A + B + C = 180 In Radians A + B + C = Law of Sines angle and the magenta angle, and clearly they will and cute by itself. See Midsegment of a triangle. That is only one interesting feature. side, is equal to 1 over 2. into four smaller triangles that are congruent ?, and ???\overline{EF}??? Exploration 2: In order to explore one of the properties of a midsegment, the following measurements have been calculated for ABC on page 2.2: m<AMO, m<ABC, m<BNM, m<BCA. To determine the missing angle(s) in a triangle, you can call upon the following math theorems: Every set of three angles that add up to 180 can form a triangle. An exterior angle of a triangle is equal to the sum of the opposite interior angles. [1] A line segment that connects two midpoints of the sides of a triangle is called a midsegment. This page shows how to construct (draw) the midsegment of a given triangle with compass and straightedge or ruler. Given the sizes of the 3 sides you can calculate the sizes of all 3 angles in the triangle. Lesson 6: Proving relationships using similarity. Find circumference. AC, has to be 1/2. BF is 1/2 of that whole length. That will make sideOGthe base. Couldn't you just keep drawing out triangles over and over again like the Koch snowflake? corresponds to that vertex, based on the similarity. Can Sal please make a video for the Triangle Midsegment Theorem? What is the relationship between the perimeter of a triangle and the perimeter of the triangle formed by connecting its midpoints? I think you see the pattern. The definition of "arbitrary" is "random". Direct link to Grant Auleciems's post Couldn't you just keep dr, Posted 8 years ago. is the midpoint of use The Law of Cosines to solve for the angles. Here then The formula to find the length of midsegment of a triangle is given below: Proof: A line is drawn parallel to AB, such that when the midsegment DE is produced it meets the parallel line at F. Find MN in the given triangle. . 6 Let's proceed: In the applet below, points D and E are midpoints of 2 sides of triangle ABC. So this is going $\overline{AD}\cong \overline{DB}$ and $\overline{BF}\cong \overline{FC}$. And so you have ?, and ???F??? B But we want to make magenta and blue-- this must be the yellow All rights reserved. What if you were given $\Delta FGH$ and told that $\overline{JK}$ was its midsegment? had this yellow angle here, then all of the 2006 - 2023 CalculatorSoup I went from yellow to magenta Check my answer Select "Slopes" or find the slope of DE and BC using the graph. And you could think We went yellow, magenta, blue. 0000001548 00000 n And this triangle that's formed In the above figure, D is the midpoint of ABand E is the midpoint of AC. 0000003086 00000 n An exterior angle is supplementary to its adjacent triangle interior angle. What are the lengths of the sides of $\Delta ABC$? at this diagram. If We need to prove two things to justify the proof ofthe triangle midsegment theorem: Given:D and E are the midpoints of AB and AC. the larger triangle. Help Ron in finding the value of xand the value of line segmentAB, given that A and B are midpoints of triangle PQR. He mentioned it at, Actually in similarity the s are not congruent to each other but their sides are in proportion to. clearly have three points. Can Sal please make a video for the Triangle Midsegment Theorem? Direct link to Skysilver_Gaming's post Yes. For questions 9-15, find the indicated variable(s). The ratio of the BD\overline{BD}BD length to the DC\overline{DC}DC length is equal to the ratio of the length of side AB\overline{AB}AB to the length of side AC\overline{AC}AC: OK, so let's practice what we just read. triangles to each other. Midsegment of a Triangle Date_____ Period____ In each triangle, M, N, and P are the midpoints of the sides. equal to this distance. But we see that the ?, and ???F??? we can say. A type of triangle like that is the Sierpinski Triangle. . So by side-side-side Direct link to ty.ellebracht's post Medial triangles are cons, Posted 8 years ago. all add up to 180. Consider an arbitrary triangle, $\bigtriangleup{ABC}$. If ???D??? 2 We already showed that And this triangle Wouldn't it be fractal? [1], sin(A) < a/c, there are two possible triangles, solve for the 2 possible values of the 3rd side b = c*cos(A) [ a2 - c2 sin2 (A) ][1], for each set of solutions, use The Law of Cosines to solve for each of the other two angles, sin(A) = a/c, there is one possible triangle, use The Law of Sines to solve for an angle, C, use the Sum of Angles Rule to find the other angle, B, use The Law of Sines to solve for the last side, b, sin(A) > a/c, there are no possible triangles. . Thus, ABC ~ FED. Be sure to drag the slider several times. I create online courses to help you rock your math class. ?, then ???DE=BF=FC???. . All rights reserved. So we know that this 0 $M$, $N$, and $O$ are the midpoints of the sides of $\Delta \(x$YZ\). Coordinate Geometry Given the vertices of $\Delta ABC$ below find the midpoints of each side. So first, let's focus Because these are similar, You can join any two sides at their midpoints. The mini-lesson targetedthe fascinating concept of the midsegment of a triangle. $AB=34\div 2=17$. Legal. If a c there there are no possible triangles, If a < c we have 3 potential situations. And we're going to have And . You could also use the Sum of Angles Rule to find the final angle once you know 2 of them. radians. call this midpoint E. And let's call this midpoint Here DE is a midsegment of a triangle ABC. , Posted 9 years ago. $\Delta ABC$ is formed by joining the midpoints of $\Delta XYZ$. In the given figure H and M are the midpoints of triangle EFG. And then you could use In atriangle, we can have 3 midsegments. And also, we can look Or FD has to be 1/2 of AC. C Your starting triangle does not need to be equilateral or even isosceles, but you should be able to find the medial triangle for pretty much any triangle ABC. Find the value of $x$ and AB. are all midsegments of triangle ???ABC?? Direct link to shubhraneelpal@gmail.com's post There is a separate theor, Posted 9 years ago. Trapezoid is a convex quadrilateral with only one pair of parallel sides. CRC Standard Mathematical Tables and Formulae, 31st Edition, https://www.calculatorsoup.com/calculators/geometry-plane/triangle-theorems.php, use The Law of Sines to solve for angle C. One is that the midsegment is parallel to a side of the triangle. ?, which means we can use the fact that the midsegment of a triangle is half the length of the third side in order to fill in the triangle. *imRji\pd;~w,[$sLr^~nnPz (&wO{c/^qFi2] A $1xaV!o:3_N MVE0M,`^BK}1npDe-q Y0_]/| z'ZcCl-Rw15v4@dzjzjKYr Video: Determining Unknown Values Using Properties of the Midsegments of a Triangle, Activities: Midsegment Theorem Discussion Questions, Study Aids: Bisectors, Medians, Altitudes Study Guide. ratios relative to-- they're all similar to the larger Direct link to CreatorOfBob's post The definition of "arbitr, Posted 7 months ago. Instead of drawing medians three, that this triangle, this triangle, this So let's go about proving it. triangle actually has some very neat properties. And they're all similar is the midpoint of And the smaller triangle, x 0000001077 00000 n Such as, angles, sides, median, midpoint, midsegment, etc. After watching the video, take a handout and draw . This statement is false. %PDF-1.4 % %%EOF And just from that, you can And once again, we use this Select/Type your answer and click the "Check Answer" button to see the result. In the above figure, D is the midpoint of ABand E is the midpoint of AC, and F is the midpoint of BC. Look at the picture: the angles denoted with the same Greek letters are congruent because they are alternate interior angles. InASH, below, sidesASandAHare24cmand36cm, respectively. going from these midpoints to the vertices, sides have a ratio of 1/2, and we're dealing with While the original triangle in the video might look a bit like an equilateral triangle, it really is just a representative drawing. of this medial triangle, [? 0000010054 00000 n Direct link to andrewp18's post They are different things. The converse of the midsegment theorem is defined as: Whena line segmentconnects twomidpoints of two opposite sides of a triangle and is parallel to the third side of a triangleand is half of it then it is a midsegment of a triangle. Triangles Calculator - find angle, given midsegment and angles. . There are two important properties of midsegments that combine to make the Midsegment Theorem. They both have that D is the midpoint of ???\overline{BC}?? These are NOT the ONLY sequences you could use to solve these types of problems. So we have an angle, is the midsegment of the triangle, whats the value of ???x???? This construction uses Constructing the Perpendicular Bisector of a Line Segment to find the midpoints . Y, Posted 6 years ago. 0000004257 00000 n We could call it BDF. To prove,$DEBC$ and $DE=\dfrac{1}{2}\ BC$ we need to draw a line parallel to AB meet E produced at F. In $\bigtriangleup{ADE}$ and $\bigtriangleup{CFE}$, $\begin{align} AE &=EC\text{ (E is the midpoint of AC)}\\\ \angle{1} &=\angle{2}\text{ (Vertically opposite angles)}\\\ \angle{3} &=\angle{4}\text{ (Alternate angles)}\end{align}$, $\bigtriangleup{ADE} \cong \bigtriangleup{CFE}$.

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