Similarity
Multiple Choice Questions (MCQ)
1. Which of the following is not a valid criterion for triangle similarity?
AA
B. ASA
C. SSS
D. SAS
Answer: B. ASA
2. If two triangles are similar, then their corresponding angles are:
Different
B. Supplementary
C. Eual
D. Complementary
Answer: C. Eual
3. In ∆ABC ∼ ∆DEF, if AB/DE = 4/3, what is the ratio of their areas?
4:3
B. 16:9
C. 2:1
D. 8:6
Answer: B. 16:9
4. If two triangles have corresponding sides in the ratio 5:2, what is the ratio of their perimeters?
25:4
B. 5:2
C. 10:3
D. 3:10
Answer: B. 5:2
5. In ∆XYZ ∼ ∆ABC, if XY = 6 cm, AB = 9 cm, and YZ = 8 cm, then what is the length of side BC?
10 cm
B. 12 cm
C. 9 cm
D. 16 cm
Answer: B. 12 cm
Short Answer Questions (SAQ)
1. Define similarity in geometry.
Answer: Similarity in geometry refers to figures that have the same shape but may differ in size. For triangles, similarity means corresponding angles are eual and corresponding sides are proportional.
2. State the AA criterion of triangle similarity.
Answer: If two angles of one triangle are eual to two angles of another triangle, then the triangles are similar (AA criterion).
3. What is the ratio of areas of two similar triangles if the ratio of their corresponding sides is 3:5?
Answer: The ratio of their areas is 3²:5² = 9:25.
Long Answer Questions (LAQ)
1. In ∆PR and ∆LMN, P = 5 cm, R = 7 cm, PR = 8 cm, and LM = 10 cm, MN = 14 cm. If ∆PR ∼ ∆LMN, find the length of LN. Also, state the similarity criterion used.
Answer: P/LM = 5/10 = 1/2
R/MN = 7/14 = 1/2
Both pairs of sides are in the same ratio, and since ∆PR ∼ ∆LMN by SSS Criterion,
⇒ PR/LN = 1/2 ⇒ LN = PR × 2 = 8 × 2 = 16 cm
Similarity Criterion used: SSS (Side-Side-Side)
2. A person of height 1.5 m casts a shadow of 0.75 m. At the same time, a pole casts a shadow of 6 m. Find the height of the pole using the concept of similar triangles.
Answer: Triangles formed by height and shadow are similar.
So, height of person / shadow = height of pole / shadow of pole
⇒ 1.5 / 0.75 = h / 6
⇒ 2 = h / 6
⇒ h = 2 × 6 = 12 m
Height of the pole = 12 m