Question

In triangle BCD, △BCD, angle C ≅ angle B, ∠C≅∠B, BD = 10, and BC = 18. Find CD.

a) 18
b) 10
c) 8
d) 5

Answer 1

The length of CD is 0 because triangle BCD is a degenerate triangle.

Step-by-step explanation:

To find CD, we can use the fact that angle C is congruent to angle B. This means that triangle BCD is an isosceles triangle. In an isosceles triangle, the base angles (angles opposite the equal sides) are congruent. Therefore, angle C is congruent to angle B and angle B is congruent to angle C. Since angle C is congruent to angle B, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Let x be the measure of angle B (or angle C). Then, we have:

x + x + 180 = 180 degrees

2x = 0

x = 0

Since x = 0, angle B and angle C are both 0 degrees. Therefore, triangle BCD is a degenerate triangle, meaning that it is a straight line. In this case, CD would have a length of 0.