Date post: | 29-Dec-2015 |
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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:
Your Turn:
Proof: Your Turn:
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).
Answer:Example 2:
Answer:Example 2:
a. Name two congruent angles. Answer:Answer:b. Name two congruent segments. Your Turn:
Properties of Equilateral sCorollary 4.3 A is equilateral iff it is equiangular. Corollary 4.4 Each of an equilateral measures 60.
Example 3a:
Answer:Add.Exterior Angle TheoremSubstitutionExample 3a:
Subtract 75 from each side.Linear pairs are supplementary.SubstitutionAnswer: 105Example 3b:
a. Find x. b. Answer: 90Answer: 30Your Turn: