Chapter 4: Congruent Triangles
This chapter focuses on isosceles and equilateral triangles, detailing their properties and relevant theorems. Isosceles triangles have at least two congruent sides, referred to as the legs, with a base and corresponding vertex and base angles. The chapter introduces important theorems, including the Isosceles Triangle Theorem, which states that the angles opposite congruent sides are also congruent. Additionally, it covers the relationships of equilateral triangles and their equiangular properties. Understanding these concepts is essential for geometric problem-solving.
Chapter 4: Congruent Triangles
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Presentation Transcript
Chapter 4:Congruent Triangles Section 4-5: Isosceles and Equilateral Triangles
Objective • To use and apply properties of isosceles triangles.
Vocabulary • Legs of an isosceles triangle • Base of an isosceles triangle • Vertex angle of an isosceles triangle • Base angles of an isosceles triangle • corollary
Isosceles Triangles • Recall: an isosceles triangle is a triangle with at least two congruent sides. • Parts of an isosceles triangle: • The congruent sides of an isosceles triangle are the legs. • The third side is the base. • The two congruent sides form the vertex angle. • The other two angles are the base angles.
Theorem 4-3:“Isosceles Triangle Theorem” • If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Theorem 4-4:“Converse of Isosceles Triangle Theorem” • If two angles of a triangle are congruent, then the sides opposite the angles are congruent.
Theorem 4-5 • The bisector of the vertex angle is the perpendicular bisector of the base.
Corollary • A corollary is a statement that follows immediately from a theorem.
Corollary to Theorem 4-3 • If a triangle is equilateral, then the triangle is equiangular.
Corollary to Theorem 4-4 • If a triangle is equiangular, then the triangle is equilateral.
