Answer to Question #88286 in Geometry for Melody

Question

In the diagram, GB = 2x + 3..
What is GB?
https://media.edgenuity.com/evresources/8101/8101-04/8101-04-05/8101-04-05-assessment/8101-04-05-25-image1.png

Answer 1

1. From the figure we see that:

1) FC = EC

2) FB = DB = DA = EA сonsequently FB + DB = DA + EA and FD = ED

3) CD - common side

SSS theorem: If three pairs of sides of two triangles are equal in length, then the triangles are congruent.

Consequently: CBE = CDF - a congruence of triangles.

2. If triangles CBE and CDF are equal, then GB = GA, since they are essentially the same line (which extends from one point on the common side of the triangles and divides the opposite leg in half).

GB = GA

2x+3 = x+9

2x-x = 9-3

x=6

GB = 2x+3 = 2*6 + 3 = 15

GB = 15