Questions and Answers
An isosceles triangle is always an _________ triangle.
equilateral
Why are those 2 triangles equal?
An equilateral triangle has at least 2 congruent sides, which makes it also an isosceles.
If a triangle is ________, then it is an isosceles triangle.
equilateral
What are the congruent sides called in an isosceles triangle?
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What is the non-congruent side called in an isosceles triangle?
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What is the angle called that is the common endpoint of the congruent sides in an isosceles triangle?
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What are the congruent angles called in an isosceles triangle?
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Equilateral triangles are equiangular.
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Each angle of an equilateral triangle equals how many degrees?
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The measures of the angles in an equilateral triangle are congruent.
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What is an isosceles triangle?
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If a triangle has 2 congruent sides, then the angles opposite those sides are also congruent.
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If a triangle has 2 congruent angles, the sides opposite those angles are also congruent.
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Study Notes
Isosceles and Equilateral Triangles Overview
- An isosceles triangle has at least two congruent sides, while an equilateral triangle has all three sides congruent.
- All equilateral triangles are isosceles, but not all isosceles triangles are equilateral.
Congruent Sides and Angles
- In an isosceles triangle, the two equal sides are referred to as legs, and the side opposite them is called the base.
- The common angle at the endpoint of the legs is known as the vertex angle.
- The angles adjacent to the base are called base angles and are also congruent.
Equilateral Triangle Theorems
- Equilateral triangles are also equiangular, meaning all three angles are equal.
- Each angle in an equilateral triangle measures 60 degrees.
- The principle that equiangular triangles are equilateral establishes a strong relationship between angles and sides in triangle properties.
Angle and Congruency Relations
- The measures of the angles in an equilateral triangle are equal, reinforcing the equiangular property.
- The Isosceles Triangle Theorem (ITT) asserts that if a triangle has two congruent sides, then the angles opposite those sides must also be congruent.
- The Converse of the Isosceles Triangle Theorem states that if a triangle has two congruent angles, the sides opposite those angles are congruent as well, illustrating a fundamental property of triangles.
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Test your knowledge on the properties of isosceles and equilateral triangles with these flashcards. Understand the definitions and relationships between these two types of triangles through engaging questions and answers.
