Questions and Answers
Which properties belong to all isosceles triangles? Check all that apply.
What is the value of x?
70
Which fact helps you prove the isosceles triangle theorem?
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.
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What is the length of PR?
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What is the value of x if the vertex angle of an isosceles triangle is 42°?
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What is the measure of each base angle if a vertex angle measures 42°?
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What is the measure of ∠NLM?
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What is the measure of ∠WYX in triangle WXY where two angles are given?
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Yin is correct in saying that triangle ABC is equilateral if x = 19.
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What is always true about the angles of an isosceles triangle?
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What is the measure of a base angle if the vertex angle of an isosceles triangle measures 40°?
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What is true about the measure of angle B in triangle ABC which is isosceles?
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What is the missing reason in the proof by contradiction assuming ∠B ≅ ∠C?
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What is the length of line segment AC in triangle ABC?
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What is the measure of angle K in triangle KNM where angle N is the vertex?
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What is the measure of a base angle in triangle ABC if it is an isosceles right triangle?
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What is true of any triangle formed by points U, V, and a point on RT, given RT is a perpendicular bisector?
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What is true about triangle AMB, given that triangle ABC is isosceles and point M is the midpoint of the hypotenuse?
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In triangle XYZ, 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.
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Study Notes
Properties of Isosceles Triangles
- Base angles in isosceles triangles are congruent.
- The sides opposite the base angles are equal in length.
- The vertex angle bisector is also the perpendicular bisector of the base.
Angle Measures
- The measure of the vertex angle can be determined to find the base angles.
- For a vertex angle of 42°, each base angle calculates to 69°.
- Conclusion from measures: If m∠ABC = 64° and both base angles equal, the triangle is not equilateral.
Triangle Relationships
- In triangle ABC, if m∠ABC is greater than m∠ACB, side AB is longer than side AC.
- Converse applies: If two angles are congruent, the opposite sides are also congruent.
Proof Techniques
- To prove AB ≅ AC when ∠B ≅ ∠C, use the converse of the triangle parts relationship theorem.
Triangle Types
- Isosceles triangles can be right triangles where base angles measure 45° each.
- A triangle where Y is twice the base angle results in angle Y being a right angle, and the other base angles measuring 45°.
Perpendicular Bisector Properties
- A triangle created with a point on the perpendicular bisector of a side results in an isosceles triangle.
Isosceles Triangle Characteristics
- At least two angles of an isosceles triangle are always congruent.
- In any isosceles triangle, identifying the measures of angles leads to understanding relationships between sides and angles.
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Description
This quiz focuses on the properties and theorems associated with isosceles triangles. It challenges your understanding of key concepts like congruent angles and sides. Test your knowledge on the foundational aspects of isosceles triangles through flashcards.
