Question

mark each shape that always has the following properties.
property | parallelogram | rectangle | rhombus | square | trapezoid | isosceles trapezoid | kite

1. both pairs of opp. sides are ≅ | | | | | | |
2. diagonals are ≅ | | | | | | |
3. diagonals are perpendicular | | | | | | |
4. diagonals bisect each other | | | | | | |
5. consecutive angles are supplementary | | | | | | |
6. both pairs of opposite ∠’s are ≅ | | | | | | |
7. ∠’s are ≅ | | | | | | |

Answer:

To solve this, we analyze each property for each quadrilateral:

Property 1: Both pairs of opp. sides are ≅

• Parallelogram: Yes (definition of parallelogram).
• Rectangle: Yes (a rectangle is a parallelogram with right angles, so opposite sides are congruent).
• Rhombus: Yes (all sides are congruent, so opposite sides are too).
• Square: Yes (a square is a rhombus and a rectangle, so opposite sides are congruent).
• Trapezoid: No (only one pair of parallel sides, not necessarily congruent).
• Isosceles Trapezoid: No (only one pair of parallel sides, legs are congruent, but not both pairs of opposite sides).
• Kite: No (two pairs of adjacent sides congruent, not opposite sides).

Property 2: Diagonals are ≅

• Parallelogram: No (diagonals bisect each other but aren’t necessarily congruent).
• Rectangle: Yes (diagonals of a rectangle are congruent).
• Rhombus: No (diagonals are perpendicular but not necessarily congruent).
• Square: Yes (a square is a rectangle, so diagonals are congruent).
• Trapezoid: No (diagonals not necessarily congruent).
• Isosceles Trapezoid: Yes (diagonals of an isosceles trapezoid are congruent).
• Kite: No (diagonals are perpendicular, not congruent).

Property 3: Diagonals are perpendicular

• Parallelogram: No.
• Rectangle: No (diagonals are congruent but not perpendicular).
• Rhombus: Yes (diagonals of a rhombus are perpendicular).
• Square: Yes (a square is a rhombus, so diagonals are perpendicular).
• Trapezoid: No.
• Isosceles Trapezoid: No.
• Kite: Yes (diagonals of a kite are perpendicular).

Property 4: Diagonals bisect each other

• Parallelogram: Yes (definition of parallelogram).
• Rectangle: Yes (a rectangle is a parallelogram, so diagonals bisect each other).
• Rhombus: Yes (a rhombus is a parallelogram, so diagonals bisect each other).
• Square: Yes (a square is a parallelogram, so diagonals bisect each other).
• Trapezoid: No (diagonals intersect but don’t bisect each other).
• Isosceles Trapezoid: No (diagonals intersect but don’t bisect each other).
• Kite: No (diagonals intersect at right angles, but one diagonal is bisected, not both).

Property 5: Consecutive angles are supplementary

• Parallelogram: Yes (consecutive angles in a parallelogram are supplementary).
• Rectangle: Yes (all angles are 90°, so consecutive angles are supplementary).
• Rhombus: Yes (a rhombus is a parallelogram, so consecutive angles are supplementary).
• Square: Yes (all angles are 90°, so consecutive angles are supplementary).
• Trapezoid: Yes (consecutive angles between the bases are supplementary).
• Isosceles Trapezoid: Yes (consecutive angles between the bases are supplementary).
• Kite: No (consecutive angles not necessarily supplementary).

Property 6: Both pairs of opposite ∠s are ≅

• Parallelogram: Yes (opposite angles in a parallelogram are congruent).
• Rectangle: Yes (all angles are 90°, so opposite angles are congruent).
• Rhombus: Yes (a rhombus is a parallelogram, so opposite angles are congruent).
• Square: Yes (all angles are 90°, so opposite angles are congruent).
• Trapezoid: No (only one pair of parallel sides, opposite angles not necessarily congruent).
• Isosceles Trapezoid: No (base angles are congruent, but not both pairs of opposite angles).
• Kite: No (one pair of opposite angles congruent, not both pairs).

Now, we mark “Yes” (✓) or “No” (✗) for each property and shape:

Property	Parallelogram	Rectangle	Rhombus	Square	Trapezoid	Isosceles Trapezoid	Kite
2	✗	✓	✗	✓	✗	✓	✗
3	✗	✗	✓	✓	✗	✗	✓
4	✓	✓	✓	✓	✗	✗	✗
5	✓	✓	✓	✓	✓	✓	✗
6	✓	✓	✓	✓	✗	✗	✗

Final Table (Marked):

Property	Parallelogram	Rectangle	Rhombus	Square	Trapezoid	Isosceles Trapezoid	Kite
2	✗	✓	✗	✓	✗	✓	✗
3	✗	✗	✓	✓	✗	✗	✓
4	✓	✓	✓	✓	✗	✗	✗
5	✓	✓	✓	✓	✓	✓	✗
6	✓	✓	✓	✓	✗	✗	✗