Question

Since it is given that AB ≅ AC, it must also be true that AB = AC. Assume ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other. If m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem. For the same reason, if m∠B < m∠C, then AC < AB. This is a contradiction to what is given. Therefore, it can be concluded that ________.

Answer 1

We are given that ΔABC is isosceles with AB ≅ AC. Using the definition of congruent line segments, we know that

✔ AB = AC

.

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

✔ triangle parts relationship theorem

.

However, this contradicts the given information that

✔ side AB is congruent to side AC

. Therefore,

✔ angle B is congruent to angle C

, 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.

Explanation:

edge 2020

Answer 2

Since it is given that AB ≅ AC, it must also be true that AB = AC. Assume ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other. If m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem. For the same reason, if m∠B < m∠C, then AC < AB. This is a contradiction to what is given. Therefore, it can be concluded that


Answer: Angle (B) is Congruent to Angle (C)

Hope it helps