Base Angles Theorem Flashcards

Questions and Answers

What is a scalene triangle?

A triangle with sides that are unequal in length (correct)

A triangle with 3 sides of the same length

A triangle with at least 2 congruent sides

A triangle with 3 interior angles that are less than 90 degrees

What defines an isosceles triangle?

A triangle with sides that are unequal in length

A triangle with at least 2 congruent sides (correct)

A triangle with 3 equal interior angles

A triangle with one angle greater than 90 degrees

What is an equilateral triangle?

A triangle with one angle that is exactly 90 degrees

A triangle with at least 2 congruent sides

A triangle with 3 sides of the same length (correct)

A triangle with sides that are unequal in length

What is an acute triangle?

A triangle with 3 interior angles that are less than 90 degrees Signup and view all the answers

What characterizes an obtuse triangle?

A triangle with one angle greater than 90 degrees Signup and view all the answers

What defines a right triangle?

A triangle with one angle that is exactly 90 degrees Signup and view all the answers

What is an equiangular triangle?

A triangle with three equal interior angles of 60 degrees Signup and view all the answers

What are the two congruent sides of an isosceles triangle called?

legs Signup and view all the answers

What is the non-congruent side of an isosceles triangle called?

base Signup and view all the answers

What is formed by the two legs of an isosceles triangle?

vertex angle Signup and view all the answers

What are the two angles adjacent to the base of an isosceles triangle called?

base angles Signup and view all the answers

What does the Base Angles Theorem state?

If 2 sides of a triangle are congruent, then the angles opposite the 2 sides are congruent. Signup and view all the answers

What does the Converse of Base Angles Theorem state?

If 2 angles of a triangle are congruent, then the sides opposite the angles are congruent. Signup and view all the answers

What does the Corollary to Base Angles Theorem state?

If a triangle is equilateral, then it is also equiangular. Signup and view all the answers

What does the Corollary to Converse of Base Angles Theorem state?

If a triangle is equiangular, then it is also equilateral. Signup and view all the answers

What does the SAS Theorem state?

If an angle of one triangle is congruent to an angle of a second triangle, and the sides that include the two angles are proportional, then the triangles are congruent. Signup and view all the answers

What does the CPCTC theorem stand for?

Corresponding Parts of Congruent Triangles are Congruent. Signup and view all the answers

What is the reflexive property?

A quantity is congruent (equal) to itself. Signup and view all the answers

Study Notes

Triangle Types

Scalene Triangle: All sides are of different lengths.
Isosceles Triangle: At least two sides are congruent.
Equilateral Triangle: All three sides are equal, and each angle measures 60 degrees.
Acute Triangle: All three interior angles are less than 90 degrees.
Obtuse Triangle: One interior angle exceeds 90 degrees.
Right Triangle: One interior angle is exactly 90 degrees.

Isosceles Triangle Properties

Legs: The two congruent sides of an isosceles triangle.
Base: The non-congruent side opposite the vertex angle.
Vertex Angle: The angle formed by the two legs.
Base Angles: The two angles adjacent to the base.

Theorems and Corollaries

Base Angles Theorem: States that in a triangle with two congruent sides, the angles opposite those sides are also congruent.
Converse of Base Angles Theorem: If two angles in a triangle are congruent, then the sides opposite those angles are congruent.
Corollary to Base Angles Theorem: In an equilateral triangle, all angles are also equal (equiangular).
Corollary to Converse of Base Angles Theorem: If a triangle is equiangular, then it must also be equilateral.

Triangle Congruence Theorems

SAS Theorem (Side-Angle-Side): States that if an angle of one triangle is congruent to an angle of another triangle and the included sides are proportional, the triangles are congruent.
CPCTC Theorem: Asserts that if two triangles are congruent, any pair of corresponding parts (sides or angles) are also congruent.

Basic Properties

Reflexive Property: Asserts that any quantity is congruent to itself, symbolized as a = a.

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Description

Test your knowledge of triangle properties with these flashcards focused on the Base Angles Theorem. Each card presents a definition for different types of triangles including scalene, isosceles, equilateral, and acute triangles. Perfect for geometry students looking to reinforce their understanding.