Triangle Inequalities

Question 1

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

Revolt · Accepted Answer

AB = AC

Question 2

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 .

Revolt · Accepted Answer

triangle parts relationship theorem

Question 3

However, this contradicts the given information that . Therefore, , which is what we wished to prove.

Revolt · Accepted Answer

side AB is congruent to side AC

Question 4

However, this contradicts the given information that . Therefore, , which is what we wished to prove.

Revolt · Accepted Answer

angle B is congruent to angle C

Question 5

We are given that ∠B ≅ ∠C. Assume segment AB is not congruent to .

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segment AC

Question 6

If AB > AC, then m∠C > m∠B by the . If AB < AC, then m∠C < m∠B by the converse of the triangle parts relationship theorem.

Revolt · Accepted Answer

converse of the triangle parts relationship theorem

Question 7

But by the definition of congruent, we know the measure of angle B equals the measure of by the given statement. Therefore, we have a contradiction: AB = AC, and AB ≅ AC.

Revolt · Accepted Answer

angle C

Triangle Inequalities Answers

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