Congruence (SSS/SAS/ASA/AAS/RHS), properties MCQs

Q1. Which of the following is NOT a valid criterion for triangle congruence?

• A.SSA (two sides and a non-included angle)
• B.SAS
• C.ASA
• D.RHS

Answer: A. SSA (two sides and a non-included angle)

To see why, recall that SSA is the ambiguous case and not a general congruence criterion. The valid criteria are SSS, SAS, ASA, AAS, RHS. Hence the answer is A) SSA (two sides and a non-included angle).

Q2. In triangle ABC, angle A = 90°. Then which inequality is FALSE?

• A.BC < AB + AC and BC ≥ AB or AC alone
• B.AB < BC
• C.AC < BC
• D.BC ≥ AB + AC

Answer: D. BC ≥ AB + AC

Given 90 °, asked for the unknown. Apply the standard chapter relation to the data. BC is the hypotenuse, larger than each leg but, by triangle inequality, strictly less than AB + AC. So option D) BC ≥ AB + AC.

Q3. In triangle ABC, AB = 7, BC = 9. Which of the following CANNOT be a possible integral length of AC?

• A.1
• B.3
• C.10
• D.15

Answer: A. 1

Which principle settles this? Triangle inequality requires |9 − 7| < AC < 9 + 7, i.e. 2 < AC < 16. Integers allowed: 3, 4, …, 15. The value 1 violates AC > 2. Pick: A) 1.