Triangles and Their Side Lengths

Question 1

Which properties belong to all isosceles triangles? Check all that apply.The base angles are congruent.All three angles are congruent.The two sides opposite the base angles are congruent.All three sides are congruent.The bisector of the vertex angle is the perpendicular bisector of the base.

Revolt · Accepted Answer

The base angles are congruent.; The two sides opposite the base angles are congruent.; The bisector of the vertex angle is the perpendicular bisector of the base.

Question 2

What is the value of x?

Revolt · Accepted Answer

70

Question 3

Which fact helps you prove the isosceles triangle theorem, which states that the base angles of any isosceles triangle have equal measure?

Revolt · Accepted Answer

If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

Question 4

CD bisects ∠ACB. Which statements must be true? Check all that apply.

Revolt · Accepted Answer

AD = BD; m∠ACD = m∠BCD; m∠CDA = m∠CDB

Question 5

Question 6

Revolt · Accepted Answer

111296

Question 6

The vertex angle of an isosceles triangle measures 42°. A base angle in the triangle has a measure given by (2x + 3)°. What is the value of x? What is the measure of each base angle? x = Each base angle measures °.

Revolt · Accepted Answer

Part 1: 33; Part 2: 69

Question 7

Question 8

Revolt · Accepted Answer

29 degrees

Question 8

Triangle WXY is isosceles. ∠YWX and ∠YXW are the base angles. YZ bisects ∠WYX.m∠XYZ = (15x)°. m∠YXZ = (2x + 5)°. What is the measure of ∠WYX?

Revolt · Accepted Answer

150°

Question 9

In triangle ABC, m∠ABC = (4x – 12)° and m∠ACB = (2x + 26)°. Yin says that if x = 19, the triangle must be equilateral. Is he correct? Justify your answer.

Revolt · Accepted Answer

No. The angles are 64°, 64°, and 52°, so the triangle is isosceles but not equilateral.

Triangles and Their Side Lengths Answers

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