Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: G-SRT.B.4, G-SRT.B.5 · Level: Grade 10 Geometry
Question 1 Similar triangle ratios (2 points)
△PQR ∼ △XYZ, with PQ = 9, XY = 15 and QR = 12. Find the scale factor from △PQR to △XYZ (1 point) and YZ (1 point).
Question 2 Choose the criterion (3 points)
Decide whether the two triangles are similar. If they are, name the criterion.
- Triangle 1 has angles 55° and 80°. Triangle 2 has angles 55° and 45°. (1 point)
- Triangle 1 has sides 4, 6 and 9. Triangle 2 has sides 6, 9 and 13.5. (1 point)
- Triangle 1 has sides 5 and 8 with a 40° angle between them. Triangle 2 has sides 10 and 12 with a 40° angle between them. (1 point)
Question 3 Side-splitter lengths (3 points)
DE ∥ BC in △ABC. AD = 6, DB = 10 and AE = 9.
- Find EC. (1 point)
- Find AC. (1 point)
- If BC = 32, find DE. (1 point)
Question 4 Converse of the side-splitter theorem (2 points)
In △ABC, D is on AB and E is on AC, with AD = 4.5, DB = 6, AE = 6 and EC = 8. Is DE parallel to BC? Show your work.
Question 5 Altitude to the hypotenuse (3 points)
A right triangle has legs 9 and 12 and hypotenuse 15. The altitude to the hypotenuse is drawn.
- Find the altitude using area. (1 point)
- Find the two pieces of the hypotenuse. (1 point)
- Verify that the altitude squared equals the product of the pieces. (1 point)
Question 6 Prove similar triangles (3 points)
Given: AB ∥ DE, and segments AD and BE intersect at C. Prove: △ABC ∼ △DEC.
Question 7 Mirror measurement (2 points)
A person with eye height 1.5 meters stands 3 meters from a mirror on the ground. The mirror is 40 meters from a tower. Write the proportion for the tower height h (1 point) and find h (1 point).
Question 8 Parallel lines and transversals (2 points)
Three parallel roads are cut by two straight paths. On the first path the segments are 80 meters and 120 meters. On the second path the first segment is 70 meters. Find the second segment on the second path.
