Isosceles Triangles

Question 1

Complete the paragraph proof.

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✔ segment AC; We are given that ∠B ≅ ∠C. Assume segment AB is not congruent to .: segment AC; 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.: converse of the triangle parts relationship theorem; 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.: angle C

Question 2

X contradiction✔ converse of the triangle parts relationship theoremisosceles triangle theorem

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✔ converse of the triangle parts relationship theorem

Question 3

angle A✔ angle CX segment AC

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✔ angle C

Question 4

Adjust point D so the measure of angle BAD is equal to the measure of angle CAD. Which statements are true? Check all that apply.AD bisects ∠BAC. AD bisects BC.AD forms right angles with BC.AD is perpendicular to BC.AD is the perpendicular bisector of BC.

Revolt · Accepted Answer

AD bisects ∠BAC.; AD bisects BC.; AD forms right angles with BC.; AD is perpendicular to BC.; AD is the perpendicular bisector of BC.

Question 5

Consider isosceles ΔXYZ.

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n: 3; 39

Question 6

What is the measure of leg XY? ft

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39

Question 7

What is the measure of leg XZ? ft

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39

Question 8

ZX bisects ∠WZY. If the measure of ∠YXZ is (6m – 12)°, what is the value of m?

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17

Question 9

Complete the paragraph proof.

Revolt · Accepted Answer

We are given that ∠B ≅ ∠C. Assume segment AB is not congruent to .: segment AC; 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.: converse of the triangle parts relationship theorem; 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.: angle C

Question 10

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

Isosceles Triangles Answers

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