Decide whether each statement is always true sometimes true

Decide whether each statement is always true, sometimes true, or never true. If a statement is sometimes true, sketch an example of when it is true and an example of when it is not. A square is a rectangle. A parallelogram is a rectangle. A trapezoid is a kite. A kite is a rhombus. A square is a kite. A rectangle is a square. A rectangle is a parallelogram. A kite is a trapezoid. A rhombus is a kite. A kite is a square k. A right triangle is an isosceles triangle. An isosceles triangle is a right triangle An acute triangle is a scalene triangle. A scalene triangle is an acute triangle.

Solution

(a) We know that square belongs to rectangle familty of quadrilaterals, therefore, a square is a rectangle. hence, True

(b) Rectangles can have unequal sides, but squares cannot, therefore, not all rectangles are squares. Hence, False

(c) Parallelogram may or maynot have all angles 90 degrees, but rectangle must have all four angles equal to 90 degrees, therefore, not all parallelograms are rectangles. Hence, False.

(d) Rectangle is a parallelogram because opposite sides are parellel to each other and equal in length. Therefore, this statement is True.

(e) Trapezoid doesn\'t have any resemblence with kite whatsoever, therefore, False

(f) Kite doesn\'t have any resemblence with Trapezoid whatsoever, therefore, False

(g) A kite may or maynot be a rhombus because not all its sides are always equal. Therefore, false.

(h) A rhombus is a special kind of kite with all sides equal, therefore, True.

(i) Square is a special case of kite when all sides are equal and all angles are 90 degrees. True.

(j) Since kite may not always have all angles or sides equal, therefore, False.

(k) Not necessarily. Only 90-45-45 is a special case, therefore, not always true. False.

(l) This is also not true. Only 90-45-45 is a special case. Therefore, False.

(j) Not necessarily. Therefore, False

(k) Not necessarily. Therefore, False.