Similar figures and similar triangles MCQs

Q1. Which pair is ALWAYS similar?

• A.any two rectangles
• B.any two circles
• C.any two parallelograms
• D.any two isosceles triangles

Answer: B. any two circles

Textbook fact: All circles have the same shape, hence always similar. Translating to the choices: Correct. The other choices: option A) 'any two rectangles' is incorrect: Rectangles can have different aspect ratios; option C) 'any two parallelograms' doesn't hold - Parallelograms vary in angle and ratio; option D) 'any two isosceles triangles' misses the point - Their apex angles can differ. Thus the correct option is B) any two circles.

Q2. Which is necessary AND sufficient for two triangles to be similar?

• A.equal perimeters
• B.equal areas
• C.corresponding angles equal (which also makes sides proportional)
• D.only one pair of equal sides

Answer: C. corresponding angles equal (which also makes sides proportional)

Eliminate first - option A) 'equal perimeters' fails since Equal perimeters do not imply similarity; option B) 'equal areas' doesn't hold - Equal areas do not imply similarity; option D) 'only one pair of equal sides' is wrong because One equal side pair is not enough. That leaves only option C). Confirm with the chapter rule: Equiangular triangles are similar (AA), which also forces proportional sides (math, chapter 'Triangles'). Answer: C) corresponding angles equal (which also makes sides proportional).

Q3. Which is sufficient to conclude triangle ABC ~ triangle DEF?

• A.AB = DE only
• B.angle A = angle D and angle B = angle E
• C.AB + BC = DE + EF
• D.area ABC = area DEF

Answer: B. angle A = angle D and angle B = angle E

Concept involved: Two equal angle pairs => AA similarity. Mapping the concept onto the options: Correct. Ruling out the other options: option A) 'AB = DE only' fails since One equal side is insufficient; option C) 'AB + BC = DE + EF' fails since Equal perimeters do not imply similarity; option D) 'area ABC = area DEF' misses the point - Equal area does not give similarity. Hence the correct option is B) angle A = angle D and angle B = angle E.