all squares are rhombi. *
true
false

all rhombi are squares. *
true
false

the legs of a trapezoid are always parallel. *
true
false

check are statements that are always true for rectangles: *
consecutive sides are perpendicular
opposite sides are congruent
consecutive sides are congruent
consecutive angles are supplementary
diagonals are perpendicular
diagonals bisect each other
diagonals are congruent
opposite sides are parallel
opposite angles are congruent

Question

all squares are rhombi. *
true
false

all rhombi are squares. *
true
false

the legs of a trapezoid are always parallel. *
true
false

check are statements that are always true for rectangles: *
consecutive sides are perpendicular
opposite sides are congruent
consecutive sides are congruent
consecutive angles are supplementary
diagonals are perpendicular
diagonals bisect each other
diagonals are congruent
opposite sides are parallel
opposite angles are congruent

Accepted Answer

### Question 1: All squares are rhombi.
# Brief Explanations:
A rhombus is defined as a quadrilateral with all sides equal in length and opposite sides parallel. A square has all sides equal and opposite sides parallel (and also has right angles). Since a square meets the criteria of a rhombus, all squares are rhombi.
# Answer:
True

### Question 2: All rhombi are squares.
# Brief Explanations:
A rhombus requires all sides to be equal and opposite sides parallel, but its angles do not have to be right angles. A square is a special type of rhombus with right angles. There are rhombi (e.g., a rhombus with angles of 60° and 120°) that are not squares, so not all rhombi are squares.
# Answer:
False

### Question 3: The legs of a trapezoid are always parallel.
# Brief Explanations:
A trapezoid is defined as a quadrilateral with at least one pair of parallel sides (called bases). The legs are the non - parallel sides. So the legs of a trapezoid are not always parallel.
# Answer:
False

### Question 4: Check the statements that are ALWAYS true for rectangles.
# Brief Explanations:
- **Consecutive sides are perpendicular**: In a rectangle, all angles are right angles (90°), so consecutive sides (which form the angles) are perpendicular. This is true.
- **Opposite sides are congruent**: By the definition of a rectangle, opposite sides are equal in length, so this is true.
- **Consecutive sides are congruent**: In a rectangle, consecutive sides can have different lengths (e.g., a rectangle with length 5 and width 3), so this is false.
- **Consecutive angles are supplementary**: In a rectangle, each angle is 90°, and 90°+90° = 180°, so consecutive angles are supplementary. This is true.
- **Diagonals are perpendicular**: In a rectangle, diagonals are equal in length and bisect each other, but they are not perpendicular (except in the special case of a square, which is a type of rectangle, but not all rectangles are squares). So this is false.
- **Diagonals bisect each other**: In a parallelogram (and a rectangle is a parallelogram), the diagonals bisect each other. This is true.
- **Diagonals are congruent**: One of the properties of a rectangle is that its diagonals are equal in length. This is true.
- **Opposite sides are parallel**: A rectangle is a type of parallelogram, and in a parallelogram, opposite sides are parallel. This is true.
- **Opposite angles are congruent**: In a parallelogram (and a rectangle is a parallelogram), opposite angles are equal. Since all angles in a rectangle are 90°, opposite angles are congruent. This is true.

# Answer:
- Consecutive sides are perpendicular
- Opposite sides are congruent
- Consecutive angles are supplementary
- Diagonals bisect each other
- Diagonals are congruent
- Opposite sides are parallel
- Opposite angles are congruent

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 1: All squares are rhombi.

Answer:

Question 2: All rhombi are squares.