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# 4.6 Isosceles Triangles. Objectives Use properties of isosceles triangles Use properties of...

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4.6 Isosceles 4.6 Isosceles Triangles Triangles
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• 4.6 Isosceles Triangles

• ObjectivesUse properties of isosceles triangles Use properties of equilateral triangles

• Properties of Isosceles TrianglesThe formed by the sides is called the vertex angle. The two sides are called legs. The third side is called the base. The two s formed by the base and the legs are called the base angles. leglegbasevertex

• Isosceles Triangle TheoremTheorem 4.9 If two sides of a are , then the s opposite those sides are (if AC AB, then B C).ABC

• Example 1:

• Proof: Example 1:

• The Converse of Isosceles Triangle TheoremTheorem 4.10If two s of a are , then the sides opposite those s are (if B C, then AC AB).

• Properties of Equilateral sCorollary 4.3 A is equilateral iff it is equiangular. Corollary 4.4 Each of an equilateral measures 60.

• Example 3a:

• Subtract 75 from each side.Linear pairs are supplementary.SubstitutionAnswer: 105Example 3b:

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