Given that segment FE is parallel to segment DG, which of the following statements is NOT true?
2 answers:
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
Thus, options (A), (C) and (D) are TRUE.
Only option (B) is NOT TRUE.
Option (B) is CORRECT.
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