Question

Urgent! this is due tomorrow and I've been sick so now I'm doing catch up work. I need help understanding this I don't get it, I just need to at least solve it.

2. Use the figure below to answer the following questions. Determine if the triangles are similar. (must show work) If similar, complete the similarity statement.
​

Answer 1

1) It is to be noted that ΔEFG ~ ΔBDC. This is because the ratios of the corresponding sides are equal.

3) Since FG = 50, then CD is 80

To determine if the triangles EFG and BDC are similar, we can use the Angle-Angle (AA) Similarity Postulate. If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.

Given that the angles are similar, we can compare the ratios of the corresponding side lengths.

In triangle EFG:

FE = 40

EG = 60

In triangle BDC:

BC = 64

BD = 96


computing the ratios we have:

FE/BC = 40/64 = 5/8
EG / BD = 60/96 = 5/8

Since the ratios of corresponding sides are equal, the triangles EFG and BDC are similar.

Therefore, we can complete the statement: ΔEFG ~ ΔBDC

3) In We are given two triangles. EFG and BDC.

We are shown that they have a similar angle.

For ΔEFG the sides of the angle are:

FE = 40 and EG = 60

while the second BC = 64 and BD = 96

If in ΔEFG the length of FG = 50, then CD is derived as:

FE/BC = FG/DC

40/64 = 50/DC

Cross multiplying we have:

40 x CD = 64 x 50

CD = (64 x 50) / 40

CD = 80

Thus, it is correct to state that CD is 80.