Isosceles Triangles Assignment and Quiz

Right triangle ABC is isosceles and point M is the midpoint of the hypotenuse. What is true about triangle AMB?

It is an isosceles right triangle.

Consider the diagram and proof by contradiction. Given: △ABC with ∠B ≅ ∠C Prove: AB ≅ AC It is given that ∠B ≅ ∠C. Assume AB and AC are not congruent. If AB > AC, then m∠C > m∠B by ________. If AC > AB, then m∠B > m∠C for the same reason. However, using the given statement and the definition of congruency, we know that m∠B = m∠C. Therefore, AB = AC and AB ≅ AC. What is the missing reason in the proof?

converse of the triangle parts relationship theorem

What is the length of PR?

40

Triangle ABC is an isosceles right triangle. What is the measure of a base angle?

45°

What is the value of x?

70

What is always true about the angles of an isosceles triangle?

At least two of the angles are congruent.

Which properties belong to all isosceles triangles? Check all that apply.

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.

What is the measure of ∠NLM? m∠NLM =

29 degrees

The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?

70°

Triangle ABC is shown below. What is the length of line segment AC?

14

Triangle ABC is isosceles. What is true about the measure of angle B?

It is equal to the measure of angle C.

Triangle XYZ is isosceles. The measure of the vertex angle, Y, is twice the measure of a base angle. What is true about triangle XYZ? Check all that apply.

Angle Y is a right angle. The measure of angle Z is 45°. The perpendicular bisector of XZ creates two smaller isosceles triangles.

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

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.

RT is a perpendicular bisector of . What is true of any triangle created by points U, V, and any point on RT other than S?

It will be an isosceles triangle.

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.

No, Yin is not correct. If x = 19, the measure of angle ABC = 4(19) - 12 = 64. Therefore, the two base angles measure 64°. An equilateral triangle is equiangular, so each angle would have to measure 60° because there are 180° in a triangle.

Triangle KNM is isosceles, where angle N is the vertex. What is the measure of angle K?

25

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?

150°

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

AD = BD m∠ACD = m∠BCD m∠CDA = m∠CDB

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 = 33 Each base angle measures 69°.