Similarity Questions

Objectives: Similarity Questions

Similarity Questions

Answer the following questions:

1. In the following figure determine the pairs of equal angles and the proportional sides which make ΔAEB ~ ΔDEC.

E B C D A

2. Name two triangles similar to ΔABC in the following figure.

A B C

3. If ΔLMN ~ ΔPQR and ΔPQR ~ ΔABC, mention equal angles in ΔABC and ΔLMN, hence mention all proportional sides in ΔPQR and ΔABC. Find the ratio of proportionality for the similarity of ΔPQR and ΔABC.

4. A triangle ABC is such that CA is extended to X and BA is extended to Y so that XY // BC. Prove that AX/AC = AY/AB.

C B A X Y

5. A trapezium PQRS is such that PQ // RS. If the diagonals intersect at X, prove that PX/RX = QX/SX.

P Q R S X
Similarity Questions (6-10)

Answer the following questions:

6. Name a triangle which is similar to ΔABC in the following figure.

A B C D F M E

7. Use similarity to find the value of ED in the following figures.

B A C 6 dm 10 dm E F D 3 dm

8. If ΔPQR ~ ΔLMN and PR = 20 dm, NL = 10 dm, NM = 12 dm and LM = 9 dm, find the lengths of the other sides of ΔPQR.

9. Prove that any two equilateral triangles are similar.

10. In ΔPMT and ΔQNS, ∠PMT = ∠QSN = ∠MTP = ∠QNS.
Prove that PM × NS = QS × MT.

Reference Book: N/A

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