Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.


Given: ΔABC is isosceles; AB ≅ AC
Prove: ∠B ≅ ∠C
Triangle A B C is shown. Sides B A and A C are congruent.
We are given that ΔABC is isosceles with AB ≅ AC. Using the definition of congruent line segments, we know that .
Let’s assume that angles B and C are not congruent. Then one angle measure must be greater than the other. If m∠B is greater than m∠C, then AC is greater than AB by the .
However, this contradicts the given information that . Therefore, , which is what we wished to prove.
Similarly, if m∠B is less than m∠C, we would reach the contradiction that AB > AC. Therefore, the angles must be congruent.


Sagot :

AB = AC, they are equivalent. Since an isosceles triangle has the congruent angle property, mB = mC cannot be shown until AB=AC.

What is Isosceles triangles?

Generally, Isosceles triangles are those that have two sides that are equal in length and two angles that are also equal in size.

Hence The sides and angles theorem for triangles., and the side AB is equal to the other side AC,

In conclusion, Assuming that the base angles, mB, and mC, are of equal measure, the triangle sides and angles theorem states that segment AC is larger than AB. The bigger angle of a triangle is always opposite to the longer side, according to the theorem.

AB is congruent to AC cannot be proven unless AB=AC then,

m<B = m<C because the isosceles triangle has the congruent angle property

Read more about Isosceles triangles

https://brainly.com/question/2456591

#SPJ1