Isosceles Triangles

Question 1

Similarly, if m∠B is less than m∠C, we would reach the contradiction that AB > AC. Therefore, the angles must be congruent.

Revolt · Accepted Answer

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 . Therefore, , which is what we wished to prove.: side AB is congruent to side AC; However, this contradicts the given information that . Therefore, , which is what we wished to prove.: angle B is congruent to angle C

Question 2

Similarly, if m∠B is less than m∠C, we would reach the contradiction that AB > AC. Therefore, the angles must be congruent.

Revolt · Accepted Answer

✔ AB = AC; 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 . Therefore, , which is what we wished to prove.: side AB is congruent to side AC; However, this contradicts the given information that . Therefore, , which is what we wished to prove.: angle B is congruent to angle C

Question 3

vertical angle theorem✔ triangle parts relationship theoremX right angle theorem

Revolt · Accepted Answer

✔ triangle parts relationship theorem

Question 4

side AB is congruent to side BCX side AC is congruent to side BC✔ side AB is congruent to side AC

Revolt · Accepted Answer

✔ side AB is congruent to side AC

Question 5

✔ angle B is congruent to angle CX angle A is congruent to angle Cangle B is congruent to angle A

Revolt · Accepted Answer

✔ angle B is congruent to angle C

Isosceles Triangles Answers

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