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Question:

State whether True or False. (a) All rectangles are squares. (b) All rhombuses are parallelograms. (c) All squares are rhombuses and also rectangles. (d) All squares are not parallelograms. (e) All kites are rhombuses. (f) All rhombuses are kites. (g) All parallelograms are trapeziums. (h) All squares are trapeziums.

Solution:

(a) False. All squares are rectangles (All sides of rectangle are not equal). (b) True. Opposite sides are equal and parallel. (c) True. All sides of the rhombus are equal ∴ All squares are rhombuses. All squares are also rectangles as each interval angle measure 90°. (d) False. All squares are parallelograms as opposite sides are equal and parallel. (e) False. Kite has different lengths. (f) True. Rhombus also has two distinct consecutive pairs of sides of equal length. (g) True. Parallelogram pair of parallel sides. (h) True. All squares have a pair of parallel sides.