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Chapter 5: Q9 (page 180)

Name all the points shown that must be midpoints of the sides of the large triangle.

Short Answer

Expert verified

D and F must be the midpoints of the side AC and CB of the large triangle.

Step by step solution

01

Step 1. Consider the diagram.

Consider the large triangle ABC.

02

Step 2. State the explanation.

In ΔABC,

CF=FB (Given)

So,

F is the midpoint of BC.

(Midpoint is a point on a line segment that divides it into two equal parts.)

Also,

DF∥AB (Given)

According to Basic Proportionality Theorem,

If a line is drawn parallel to one side of a triangle such that it intersects the other sides in different points, then the other two sides are divided in the same ratio.

So,

CFFB=CDDA

As CF=FB, then,

CFFB=1

So,

1=CDDACD=DA

Thus, D is a midpoint AC.

03

Step 3. State the conclusion.

Therefore, D and F must be the midpoints of the side AC and CB of the large triangle.

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