smc

Question

Let the two base angles of a triangle be A and B, with B larger than A. The altitude to the base divides the vertex angle C into two parts, C_1 and C_2, with C_2 adjacent to side a. Then:

Accepted Answer

FIGURE Noting that side a is opposite of angle A, label the diagram as shown. From the two right triangles, B + C_2 = 90 A + C_1 = 90 Substitute to get B + C_2 = A + C_1 B - A = C_1 - C_2 The answer is C_1-C_2=B-A.