Is the following a proof? If not, why not? Theorem: The base angles of an isosceles triangle are equal. Proof: Let ABC be an isosceles triangle with sides AB = AC. Then ABC is congruent to ACB because the corresponding sides are equal: AB = AC, BC = CB, AC = AB. Here, corresponding angles are equal: in particular ̸ ABC = ̸ ACB. (You may assume the usual geometrical properties of congruent triangles.)
Is the following a proof? If not, why not? Theorem: The base angles of an isosceles triangle are equal. Proof: Let ABC be an isosceles triangle with sides AB = AC. Then ABC is congruent to ACB because the corresponding sides are equal: AB = AC, BC = CB, AC = AB. Here, corresponding angles are equal: in particular ̸ ABC = ̸ ACB. (You may assume the usual geometrical properties of congruent triangles.)
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.2: Angles And Their Relationships
Problem 39E
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8. Is the following a proof? If not, why not?
Theorem: The base angles of an isosceles triangle are equal.
Proof: Let ABC be an isosceles triangle with sides AB = AC. Then ABC is congruent to ACB because the corresponding sides are equal: AB = AC, BC = CB, AC = AB. Here, corresponding angles are equal: in particular ̸ ABC = ̸ ACB. (You may assume the usual geometrical properties of congruent triangles.)
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