Question

(30 points for all)

1. All parallelograms are rectangles. True or False
2. All rectangles are quadrilaterals. True or False
3. All rectangles are rhombuses. True or False

Answer 1

Rectangles are a specific type of parallelogram, not all rectangles are rhombuses.

Step-by-step explanation:

1. All parallelograms are rectangles. False. While all rectangles are parallelograms, not all parallelograms are rectangles. Rectangles are a specific type of parallelogram that has four right angles. Parallelograms, on the other hand, have opposite sides that are parallel and equal in length, but their angles can be any measure except 90 degrees.

2. All rectangles are quadrilaterals. True. A rectangle is a special type of quadrilateral that has four right angles. So, all rectangles are quadrilaterals.

3. All rectangles are rhombuses. False. While all rectangles are quadrilaterals, not all rectangles are rhombuses. A rhombus is a quadrilateral with all sides of equal length, but its angles may or may not be right angles. Rectangles have two pairs of parallel sides and four right angles, which are not characteristic of rhombuses.

Answer 2

Answer: (1) Sometimes, only if the parallelogram is also a rhombus. 13. A rectangle is a square. ... A square has opposite angles congruent. o Always, all parallelograms have opposite sides congruent. 16.

(2) Some rectangles may be squares, but not all rectangles have four congruent sides. All squares are rectangles however. The correct answer is that all trapezoids are quadrilaterals.

(3) Every square is a rhombus, and a rhombus can be a square, if all its angles are 90 degrees. Thus, a rhombus can be a rectangle (if the angles of the rhombus are all 90 degrees), and a rectangle can be a rhombus (if the sides of the rectangle are all equal length).

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