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RD Chapter 4 Triangles Ex 4.1 Solutions

Question - 1 : -
Fill in the blanks using the correct word given in brackets :
(i) All circles are тАжтАжтАжтАжтАж (congruent, similar).
(ii) All squares are тАжтАжтАжтАж (similar, congruent).
(iii) All тАжтАжтАжтАжтАж.. triangles are similar (isosceles, equilaterals) :
(iv) Two triangles are similar, if their corres-ponding angles are тАжтАжтАж (proportional, equal)
(v) Two triangles are similar, if their corres-ponding sides are тАжтАжтАжтАжтАж. (proportional, equal)
(vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles are тАжтАжтАжтАж. and (b) their corres-ponding sides are тАжтАжтАжтАжтАж.. (equal, proportional).

Answer - 1 : -

(i) All circles are similar.
(ii) All squares are similar.
(iii) All equilaterals triangles are similar.
(iv) Two triangles are similar, if their corresponding angles are equal.
(v) Two triangles are similar, if their corresponding sides are proportional.
(vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles are equal and (b) their corresponding sides are proportional.

Question - 2 : -
Write the truth value (T/F) of each of the following statements :
(i) Any two similar figures are congruent.
(ii) Any two congruent figures are similar.
(iii) Two polygons are similar, if their corresponding sides are proportional.
(iv) Two polygons are similar if their corresponding angles are proportional.
(v) Two triangles are similar if their corresponding sides are proportional.
(vi) Two triangles are similar if their corresponding angles are proportional.

Answer - 2 : -

(i) False : In some cases, the similar polygons can be congruent.
(ii) True.
(iii) False : Its corresponding angles must be equal also.
(iv) False : Angle are equal not proportional.
(v) True.
(vi) False : Sides should be proportional and corresponding angles should be equal.

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