Question

Given that segment FE is parallel to segment DG, which of the following statements is NOT true?
A. angle HFE is congruent to angle HGD
B. triangle HFE is congruent to triangle HGD
C. triangle HFE is similar to triangle HGD
D. The Ratio Of DG to EF is equal to the ratio of HD to HE

Answer 1

The answer is B i believe

Answer 2

Answer:  The correct option is

(B)  triangle HFE is congruent to triangle HGD.

Step-by-step explanation:  Given that the segment FE is parallel to segment DG in the figure.

We are to select the statement that is NOT true.

From the figure, we note that FE is parallel to DG and FG is a transversal, so we have

m∠HFE = m∠HGD

Again, FE is parallel to DG and ED is a transversal, so we have

m∠HEF = m∠HDG

Also, m∠EHF = m∠DHG [vertically opposite angles]

Therefore, ΔHFE is similar to ΔHGD by AAA similarity postulate.

We know that the corresponding sides of two similar triangles are proportional, so we get

$\dfrac{DG}{FE}=\dfrac{HD}{HE}.$

Thus, options (A), (C) and (D) are TRUE.

Only option (B) is NOT TRUE.

Option (B) is CORRECT.