Congruence Criteria of Triangles (SAS, ASA, SSS, RHS) MCQs

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.