Question

Help plz

If F G || B C which equation is true?

A. A D / D F = A E / E G
B. D F / F B = E G / G C
C. A D / D B = A E / E C
D. A F / F B = A G / G C

Answer 1

Answer : The true equation is, (D)

Step-by-step explanation :

According to the theorem, if a line is parallel to one side of a triangle and intersects the other two sides then it separates the sides into segment of proportional length.

As we are given that:

FG║CB

That means, option (D) is a true equation.

Option A, B and C are not true because we are not given that the DE parallel to FG or CB.

Hence, the true equation is, (D)

Answer 2

D. A F / F B = A G / G C

Explanation:

Nothing is said about segment DE being parallel to FG or BC, so any answer choices involving points D or E can be eliminated from consideration. The only remaining choice is the last choice.

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In similar triangles AGF and ACB, corresponding segments are proportional.