Q: In triangle ABC, a line DE is parallel to BC, with D on AB and E on AC. $AD=4$, $DB=2$. If $AE=6$, find $EC$ using $\frac{AD}{DB} = \frac{AE}{EC}$.

3 — $\frac{4}{2} = \frac{6}{EC}$ gives $EC = \frac{6 \times 2}{4} = 3$.

Question 1

A line is drawn parallel to one side of a triangle, cutting the other two sides. What does the proportionality theorem say about those two sides?

Accepted Answer

They are divided in the same proportion — A line parallel to one side of a triangle divides the other two sides proportionally — this is the proportionality theorem.

Question 2

The Midpoint Theorem is a special case of the proportionality theorem where the ratio of division is:

Accepted Answer

1:1 (the line bisects both sides) — The Midpoint Theorem is the case where the parallel line passes through the midpoints of both sides, dividing them in a 1:1 ratio.

Question 3

In triangle ABC, a line DE is parallel to BC, with D on AB and E on AC. $AD=4$, $DB=2$. If $AE=6$, find $EC$ using $\frac{AD}{DB} = \frac{AE}{EC}$.

Accepted Answer

3 — $\frac{4}{2} = \frac{6}{EC}$ gives $EC = \frac{6 	imes 2}{4} = 3$.

Euclidean Geometry

Sample practice questions