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Explore a comprehensive set of questions and solutions focused on isosceles triangles. This resource covers key properties, theorems, and angle relationships, providing detailed explanations and correct answers. It includes problems on congruent base angles, side lengths, angle bisectors, and proofs, suitable for high school geometry students seeking to deepen their understanding and problem-solving skills in triangle geometry. The material is designed to reinforce geometric principles and enhance analytical thinking.
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Which properties belong to all isosceles triangles? Check all that apply. - correct 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. What is the value of x? - correct answer 70 Which fact helps you prove the isosceles triangle theorem, which states that the base angles of any isosceles triangle have equal measure? - correct 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. CD bisects ∠ACB. Which statements must be true? Check all that apply. - correct answer AD = BD m∠ACD = m∠BCD m∠CDA = m∠CDB What is the length of PR? - correct answer 40 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? - correct answer x = 33 Each base angle measures 69°. What is the measure of ∠NLM?
m∠NLM = - correct answer 29 degrees 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? - correct answer 150° 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. - correct 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. What is always true about the angles of an isosceles triangle? - correct answer At least two of the angles are congruent. The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle? - correct answer 70° Triangle ABC is isosceles. What is true about the measure of angle B? - correct answer It is equal to the measure of angle C. Consider the diagram and proof by contradiction. Given: △ABC with ∠B ≅ ∠C Prove: AB ≅ AC
What is true of any triangle created by points U, V, and any point on RT other than S? - correct answer It will be an isosceles triangle. Right triangle ABC is isosceles and point M is the midpoint of the hypotenuse. What is true about triangle AMB? - correct answer It is an isosceles right triangle. 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. - correct answer Angle Y is a right angle. The measure of angle Z is 45°. The perpendicular bisector of XZ creates two smaller isosceles triangles.