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. Get the free view of Chapter 3, Triangles Mathematics 2 Geometry 9th Standard Maharashtra State Board additional questions for Mathematics Mathematics 2 Geometry 9th Standard Maharashtra State Board Maharashtra State Board,Īnd you can use to keep it handy for your exam preparation.Isosceles triangle theorem states that if two sides of a triangle are congruent, then the angles opposite to the congruent sides are also congruent. Maximum Maharashtra State Board Mathematics 2 Geometry 9th Standard Maharashtra State Board students prefer Balbharati Textbook Solutions to score more in exams. The questions involved in Balbharati Solutions are essential questions that can be asked in the final exam. Using Balbharati Mathematics 2 Geometry 9th Standard Maharashtra State Board solutions Triangles exercise by students is an easy way to prepare for the exams, as they involve solutionsĪrranged chapter-wise and also page-wise. Balbharati textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.Ĭoncepts covered in Mathematics 2 Geometry 9th Standard Maharashtra State Board chapter 3 Triangles are Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle, Remote Interior Angles of a Triangle Theorem, Isosceles Triangles Theorem, Property of 30°- 60°- 90° Triangle Theorem, Median of a Triangle, Perpendicular Bisector Theorem, Angle Bisector Theorem, Properties of inequalities of sides and angles of a triangle, Congruence of Triangles, Corollary of a Triangle, Property of Median Drawn on the Hypotenuse of Right Triangle, Exterior Angle of a Triangle and Its Property, Converse of Isosceles Triangle Theorem, Property of 45°- 45°- 90° Triangle Theorem, Similar Triangles, Similarity of Triangles. This will clear students' doubts about questions and improve their application skills while preparing for board exams.įurther, we at provide such solutions so students can prepare for written exams. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion.īalbharati solutions for Mathematics Mathematics 2 Geometry 9th Standard Maharashtra State Board Maharashtra State Board 3 (Triangles) include all questions with answers and detailed explanations. has the Maharashtra State Board Mathematics Mathematics 2 Geometry 9th Standard Maharashtra State Board Maharashtra State Board solutions in a manner that help students
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