Congruence Criteria of Triangles (SAS, ASA, SSS, RHS)Practice Questions & MCQs
Practice Congruence Criteria of Triangles (SAS, ASA, SSS, RHS) questions from Triangles (Class 9 Maths) - important MCQs with answers and step-by-step solutions. Solve the sample questions below, then practice the full set free on the RankByte app.
Congruence Criteria of Triangles (SAS, ASA, SSS, RHS)Quiz - Solve & Score
Q1. In triangle ABC, AB = 7 units, BC = 9 units and CA = 6 units. D is the mid-point of BC and AD is joined. Comparing triangles ABD and ACD, which extra single piece of information would make them congruent so that angle ADB = 90 degrees, and what is the perimeter (units) of triangle ABC?
- A.AB = AC, 22
- B.BD = DC, 22
- C.AB = AC, 16
- D.angle B = angle C, 22
Answer: A. AB = AC, 22
Q2. In triangle ABC, AB = 8 units, BC = 5 units and CA = 11 units. D is the mid-point of BC and AD is joined. Comparing triangles ABD and ACD, which extra single piece of information would make them congruent so that angle ADB = 90 degrees, and what is the perimeter (units) of triangle ABC?
- A.AB = AC, 24
- B.BD = DC, 24
- C.AB = AC, 13
- D.angle B = angle C, 24
Answer: A. AB = AC, 24
Q3. In triangle ABC, AB = 10 units, BC = 7 units and CA = 13 units. D is the mid-point of BC and AD is joined. Comparing triangles ABD and ACD, which extra single piece of information would make them congruent so that angle ADB = 90 degrees, and what is the perimeter (units) of triangle ABC?
- A.AB = AC, 30
- B.BD = DC, 30
- C.AB = AC, 17
- D.angle B = angle C, 30
Answer: A. AB = AC, 30
Reading the problem, 10, 7, 13, 90 (math, chapter 'Triangles'). What we must find: what is the perimeter (units) of triangle ABC?. The principle that connects these is - BD = DC. Substituting and simplifying: angle ADB = angle ADC = 180/2 = 90 degrees → perimeter = 10+7+13 = 30 units. So the correct choice is A) AB = AC, 30. As for the others, option B) 'BD = DC, 30' fails since BD = DC and AD common give only 2 pairs; the third must be AB = AC for SSS forcing AD perpendicular; option C) 'AB = AC, 17' fails since Perimeter adds all three sides AB+BC+CA, not two.
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