Question

Given: ΔABC is isosceles; AB ≅ AC

Prove: ∠B ≅ ∠C



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.

Answer 1

AB = AC

Triangle parts relationship theorem

side AB is congruent to side AC

angle B is congruent to angle c

Explanation:

Answer 2

Explanation:

Given: ΔABC is isosceles; AB ≅ AC

Prove: ∠B ≅ ∠C

Proof:

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

Let us 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.

Now, this contradicts the given information that the side AB is congruent to the side AC that is AB ≅ AC.

Therefore, AB ≅ AC that 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 that is angle B is congruent to angle C.

Hence proved.