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10. Select all true statements.

A. All rectangles are squares.
B. All rectangles are parallelograms.
C. All rhombuses are parallelograms.
D. All squares are rectangles.
E. All squares are rhombuses.
F. All trapezoids are parallelograms.

User Prawin
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2 Answers

19 votes
19 votes

A rectangle is a quadrilateral with four right angles. A square is a special type of rectangle where all four sides are equal in length. Therefore, statement D is true: all squares are rectangles.

A parallelogram is a quadrilateral with opposite sides that are parallel. A rectangle has opposite sides that are parallel, so statement B is true: all rectangles are parallelograms.

A rhombus is a quadrilateral with all sides of equal length. It also has opposite sides that are parallel. Since a parallelogram has opposite sides that are parallel, statement C is true: all rhombuses are parallelograms.

However, not all parallelograms are rectangles or squares. A parallelogram can have angles that are not right angles, unlike a rectangle or a square. Therefore, statement A is false: not all rectangles are squares.

Similarly, not all squares are rhombuses. While a square is a rhombus because it has all sides of equal length, a rhombus does not necessarily have all angles that are right angles like a square does. So, statement E is false: not all squares are rhombuses.

Lastly, a trapezoid is a quadrilateral with one pair of parallel sides. A parallelogram has two pairs of parallel sides, so a trapezoid is not necessarily a parallelogram. Therefore, statement F is false: not all trapezoids are parallelograms.

To summarize:

- All squares are rectangles (D is true).

- All rectangles are parallelograms (B is true).

- All rhombuses are parallelograms (C is true).

- Not all rectangles are squares (A is false).

- Not all squares are rhombuses (E is false).

- Not all trapezoids are parallelograms (F is false).

User Dingles
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23 votes
23 votes

The correct answers are:

B, D, and E.

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

A rectangle is a parallelogram with all right angles, so yes, every rectangle is a parallelogram.

A square is a parallelogram with all right angles and all congruent sides; since it is a parallelogram with all right angles, every square is a rectangle.

A rhombus is a parallelogram with all congruent sides.

Since a square is a parallelogram with all congruent sides, then every square is a rhombus.

A trapezoid is a quadrilateral with one pair of parallel sides. Since a rhombus is a parallelogram, with 2 pairs of parallel sides, rhombus are not trapezoids.

User Gretal
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3.3k points