Checkpoint: the parallel-line pair

DE is parallel to BC. AD = 6, DB = 3 and AE = 5. What is EC?

• 2.5
• 10
• 4

In the proof, triangles BDE and CDE have equal area. Why?

• They share base DE. B and C are equally far from it.
• Their sides are in one ratio, as in similar triangles.
• They have the same three angles as triangle ABC.

D is on AB and E is on AC. AD = 2.5, DB = 7.5, AE = 3 and EC = 9. Is DE parallel to BC?

• No. The lengths are different.
• Yes. Both ratios are 1/3.
• Cannot say without the angles.

A line has AD ÷ DB = 1/4 and AE ÷ EC = 2/5. What follows?

• The line is parallel to BC.
• Nothing can be said without the angles.
• The line is not parallel to BC.

Which sentence is the converse of the parallel-line theorem?

• A line parallel to one side is always half as long.
• Equal ratios on two sides make the line parallel to BC.
• A parallel to one side cuts the other two in one ratio.