The converse of the isosceles triangle theorem can be proved by using the congruence properties and properties of an isosceles triangle. How to Prove the Converse of the Isosceles Triangle Theorem? The converse of isosceles triangle theorem states that, if two angles of a triangle are equal, then the sides opposite to the equal angles of a triangle are of the same measure. What is the Converse of Isosceles Triangle Theorem? The two triangles now formed with altitude as its common side can be proved congruent by SSS congruence followed by proving the angles opposite to the equal sides to be equal by CPCT. An isosceles triangle can be drawn, followed by constructing its altitude. Isosceles triangle theorem can be proved by using the congruence properties and properties of an isosceles triangle. Isosceles triangle theorem states that, if two sides of an isosceles triangle are equal then the angles opposite to the equal sides will also have the same measure. Related ArticlesĬheck these articles related to the concept of the isosceles triangle theorem.įAQs on Isosceles Triangle Theorem What is Isosceles Triangle Theorem? Hence we have proved that, if two angles of a triangle are congruent, then the sides opposite to the congruent angles are equal. Proof: We know that the altitude of a triangle is always at a right angle with the side on which it is dropped. Let's draw a triangle with two congruent angles as shown in the figure below with the markings as indicated. Converse of Isosceles Triangle Theorem Proof We will be using the properties of the isosceles triangle to prove the converse as discussed below. This is exactly the reverse of the theorem we discussed above. The converse of isosceles triangle theorem states that if two angles of a triangle are congruent, then the sides opposite to the congruent angles are equal. Hence, we have proved that if two sides of a triangle are congruent, then the angles opposite to the congruent sides are equal. Proof: We know, that the altitude of an isosceles triangle from the vertex is the perpendicular bisector of the third side. Given: ∆ABC is an isosceles triangle with AB = AC.Ĭonstruction: Altitude AD from vertex A to the side BC. Let's draw an isosceles triangle with two equal sides as shown in the figure below. To understand the isosceles triangle theorem, we will be using the properties of an isosceles triangle for the proof as discussed below. Many of these problems take more than one or two steps, so look at it as a puzzle and put your pieces together!īelow you can download some free math worksheets and practice.Isosceles triangle theorem states that if two sides of a triangle are congruent, then the angles opposite to the congruent sides are also congruent. If you don’t remember that last step, don’t worry! You can just take two more steps and find the 3 rd angle of the bottom triangle and subtract it from 180°to find the exterior angle. We need a few pieces of the puzzle before we can find the measure of x. They ultimately want to find the measure of that exterior angle. There’s actually at least three different ways that you can answer this problem. Find a piece at a time and put them together until you reach your answer! You have to look at these problems as “puzzles” because sometimes you need to find a part that they are not asking for in order to find the final result. Let’s see if we can put these properties to work and answer a few questions. So, in EVERY equilateral triangle, the angles are always 60°. This is because all angles in a triangle always add up to 180°and if you divide this amongst three angles, they have to each equal 60°. The angles, however, HAVE to all equal 60°. The sides can measure anything as long as they are all the same. When all angles are congruent, it is called equiangular. In an equilateral triangle, all sides are congruent AND all angles are congruent. Here are some diagrams that usually help with understanding. Since two sides are congruent, it also means that the two angles opposite those sides are congruent. Well, some of these types of triangles have special properties!Īn isosceles triangle has two sides that are congruent. We’ve learned that you can classify triangles in different ways.
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