Base Angles Theorem Flashcards

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.