Question

a line parallel to the base divides other two sides proportionally

Answer 1

By Basic Proportionally Theorem Proof:

In triangle ABC, a line drawn parallel to BC cuts AB and AC at P and Q respectively.

To Prove:

AP/PB = AQ/QC

Let the point P divide AB in the ratio of l: m where l and m are natural numbers. Divide AP into 'l' and PB into 'm' equal parts. Through each of these points on AB, draw lines parallel to BC to cut AC.

PROOF: 

Step 1:Cut AP into equal parts and draw lines through these points parallel to BC.

Step 2:By intercept theorem,AQ is cut into equal parts.

Step 3:By Step 1,QC is cut into m equal parts.

Step 4:By construction,AP/PB=l/m.

Step 5:By step 2 and 3,AQ/QC=l/m.

Step 6:By step 4 and 5,AP/PB=AQ/QC

Hence the proof..