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Unformatted text preview: 57 Isosceles and Equilateral Triangles and 58 Converses
A) Theorem 54 (The Isosceles Triangle Theorem) a. If two sides of a triangle are congruent, then the angles opposite these sides are congruent.
b. Given: A B Proof: C B) Definitions a. Isosceles i. A triangle with two sides congruent
b. base angles i. the two angles that include the base vertex angle i. the angle opposite the base equilateral i. a triangle whose 3 sides are congruent scalene i. a triangle no two of whose sides are congruent equiangular i. a triangle whose 3 angles are congruent corollary c. d. e. f. g. C) a theorem which is an immediate consequence of another theorem Corollary 54.1 a. Every equilateral triangle is equiangular
i. Name each triangle with two names 1) 2) 3) 4) D) Theorem 55 (Converse of the Isosceles Triangle Theorem) a. If two angles of a triangle are congruent, then the sides opposite them are congruent E) Corollary 55.1 a. Every equiangular triangle is equilateral Converse a. What is the converse of this statement st i. If it is the 31 of October in the U.S.A, then it is Halloween. b. Converses i. Are formed by switching the hypothesis and conclusion "if and only if" F) c. i. Can be used as a shortcut if both the theorem and its converse are true ...
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This note was uploaded on 05/16/2011 for the course ALGEBRA 098 taught by Professor Johnson during the Spring '09 term at Grand Valley State.
 Spring '09
 Johnson
 Algebra

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