Question

AD and BE are medians of triangle ABC. Through D, DF is drawn parallel to BE. What is the ratio CF​

Answer 1

Step-by-step explanation:

Concept:

Basic Proportionality Theorem: If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

Calculation:

Let's draw the diagram and draw a line parallel to BE through D intersecting AC at a point G:

F1 Aman Shraddha 31.12.2020 D1

It is given that D is the mid-point of BC and E is the mid-point of AD.

By construction, DG || BF.

In ΔADG, AE : ED = AF : FG (Basic Proportionality Theorem)

But AE = ED.

⇒ AF = FG ... (1)

Also, in ΔBCF, BD : DC = FG : GC (Basic Proportionality Theorem)

But BD = DC.

⇒ FG = GC ... (2)

From (1) and (2), we get:

AF = FG = FC

⇒ AF : FC = 1 : 2.

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