Criteria for similarity of triangles MCQs

Q1. AA similarity needs how many pairs of equal angles to be stated?

• A.two
• B.one
• C.three
• D.none

Answer: A. two

NCERT fact (math, chapter 'Triangles'): Two equal angle pairs are enough (third follows). Why option A fits - Correct. Distractor analysis: option B) 'one' doesn't hold - One equal angle is not enough; option C) 'three' fails since Two suffice; the third follows from the angle sum. Final answer - A) two.

Q2. Two triangles are similar if two angles of one equal two angles of the other (NCERT):

• A.RHS criterion
• B.SSS criterion
• C.SAS criterion
• D.AA criterion

Answer: D. AA criterion

NCERT fact (math, chapter 'Triangles'): The triangles are similar by the matching criterion (AA, SAS or SSS); hence ratios of corresponding sides are equal => set up the proportion and solve for the unknown side; therefore the required length = AA criterion. Why option D fits - Correct. Distractor analysis: option A) 'RHS criterion' doesn't hold - RHS is right-triangle congruence; option B) 'SSS criterion' misses the point - SSS uses sides. Final answer - D) AA criterion.

Q3. If all three pairs of sides are proportional, the triangles are similar by (NCERT):

• A.SSS
• B.ASA
• C.AA
• D.SAS

Answer: A. SSS

Eliminate first - option B) 'ASA' doesn't hold - ASA is congruence; option C) 'AA' misses the point - AA uses angles; option D) 'SAS' is wrong because SAS needs an included angle. That leaves only option A). Confirm with the chapter rule: The triangles are similar by the matching criterion (AA, SAS or SSS); hence ratios of corresponding sides are equal => set up the proportion and solve for the unknown side; therefore the required length = SSS (math, chapter 'Triangles'). Answer: A) SSS.