Understanding Triangle Stability and Properties of Congruent Angles
This guide explores the concepts of triangle stability, including which figures are stable and why. It delves into special triangles, focusing on the Base Angles Theorem, which states that if two sides of a triangle are congruent, the angles opposite those sides are also congruent. The converse also holds true. Moreover, it discusses the relationship between equilateral and equiangular triangles and provides examples for calculating measures of interior angles and solving for unknowns in triangles.
Understanding Triangle Stability and Properties of Congruent Angles
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Presentation Transcript
Sections 4.3, 4.7, 4.8 – Using Triangles HW #20 pg. 237 #13-15, 23 pg. 267 #1-13, 15-17, 19, 23-25
Stability • Which of the following figures is stable? Why?
Special Triangles • Base Angles Theorem • If two sides of a triangle are congruent, then the angles of the opposite sides are congruent • Converse of Base Angles • If two angles of a triangle are congruent, then the sides opposite them are congruent.
Example • Which two angles in the following triangle are congruent?
Corollaries • If a triangle is equilateral, then it is equiangular. • If a triangle is equiangular, then it is equilateral.
Equilaterals • Find the measures of the three interior angles.
Example • Find x and y.
Example • Find x and y.
