Isosceles Triangles

Question 1

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

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AB = AC

Question 2

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.

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converse of the triangle parts relationship theorem

Question 3

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.

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angle C

Question 4

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

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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

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 7

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

Revolt · Accepted Answer

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Isosceles Triangles Answers

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