Triangles — Questions & Answers

Sample questions from Triangles

1. Q1. In triangle ABC, DE is parallel to BC with D on AB and E on AC. If AD = 2 cm, DB = 3 cm and AE = 4 cm, then EC is:

   • A.4 cm
   • B.8 cm
   • C.2.67 cm
   • D.6 cm✓
   Solution

   D is correct. By the basic proportionality theorem, AD/DB = AE/EC, so 2/3 = 4/EC, giving EC = 6 cm. A copies AE. B comes from doubling AE for no reason. C comes from writing the proportion upside down as 3/2 = 4/EC.

2. Q2. If two angles and the included side are equal, triangles are congruent by:

   • A.ASA✓
   • B.AAA only
   • C.SSA only
   • D.RHS only
   Solution

   ASA gives congruence.

3. Q3. In △ABC, D and E lie on AB and AC with DE ∥ BC. If AD = 4 cm, AB = 9 cm and ar(△ADE) = 16 cm², then ar(△ABC) is:

   • A.36 cm²
   • B.81 cm²✓
   • C.64 cm²
   • D.72 cm²
   Solution

   ar(ADE)/ar(ABC) = (AD/AB)² = 16/81, and since ar(ADE) = 16 cm², ar(ABC) = 81 cm².

4. Q4. If the side ratio of similar triangles is 4, their area ratio is: Verify the related triangles calculation:

   • A.16✓
   • B.4
   • C.8
   • D.64
   Solution

   Area ratio is square of side ratio: 4²=16.

5. Q5. Triangle ABC is similar to triangle PQR with AB = 4 cm, PQ = 6 cm and BC = 6 cm. Then QR is:

   • A.4 cm
   • B.9 cm✓
   • C.8 cm
   • D.12 cm
   Solution

   B is correct. Corresponding sides give AB/PQ = BC/QR, so 4/6 = 6/QR and QR = 36/4 = 9 cm. A copies AB. C comes from adding the difference of 2 to BC instead of scaling. D comes from doubling BC, which would be right only if the ratio were 1 to 2 rather than 2 to 3.

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