Fill each blank with sometimes, always, or never to make each statement true. a.) The opposite angle of a parallelogram can _ have different measures. b) The base angles of an isosceles trapezoid are supplementary. c.) Parallelograms are squares. d.) A rhombus is a trapezoid. f.) 1 pair of opposite angles in a kite is congruent. g.) A quadrilateral whose diagonals are perpendicular is a rhombus. h.) quadrilateral whose diagonals are congruent is __ a rectangle. Circle the quadrilaterals which have the property described. You may need to circle more than one. Both pairs of opposite sides are congruent. Rhombus Square Isosceles Trapezoid Parallelogram Has at least one pair of consecutive angles that is supplementary. Rhombus Square Isosceles Trapezoid Parallelogram Diagonals are perpendicular. Kite Rhombus Square Isosceles Trapezoid Parallelogram Diagonals bisect one another. Kite Rhombus Square Isosceles Trapezoid Parallelogram A quadrilateral has two congruent diagonals which bisect each other. Name the most specific quadrilateral that is can be proven to be. Draw a diagram may help.
The Correct Answer and Explanation is :
Here are the correct answers for each statement, followed by explanations:
a) The opposite angle of a parallelogram can never have different measures.
- Explanation: In a parallelogram, opposite angles are always congruent, meaning they must always have the same measure.
b) The base angles of an isosceles trapezoid are always supplementary.
- Explanation: In an isosceles trapezoid, the non-parallel sides are congruent, and the base angles (the angles adjacent to each base) are supplementary, meaning their sum is 180°.
c) Parallelograms are sometimes squares.
- Explanation: A square is a special type of parallelogram where all sides and angles are congruent. So, while every square is a parallelogram, not all parallelograms are squares.
d) A rhombus is never a trapezoid.
- Explanation: A trapezoid is a quadrilateral with one pair of parallel sides, while a rhombus has all sides congruent and opposite sides parallel. Therefore, a rhombus cannot be a trapezoid.
f) 1 pair of opposite angles in a kite always is congruent.
- Explanation: In a kite, one pair of opposite angles (the angles formed by the non-congruent sides) are always congruent.
g) A quadrilateral whose diagonals are perpendicular is sometimes a rhombus.
- Explanation: Diagonals of a rhombus are always perpendicular, but there are other quadrilaterals (like a kite) whose diagonals are perpendicular but are not rhombuses.
h) A quadrilateral whose diagonals are congruent is always a rectangle.
- Explanation: A rectangle is a quadrilateral with congruent diagonals. While some other quadrilaterals (such as squares) also have congruent diagonals, a rectangle is the most specific type of quadrilateral with this property.
Quadrilateral properties:
- Both pairs of opposite sides are congruent:
- Rhombus, Square, Parallelogram
- Explanation: Parallelograms (and specifically squares and rhombuses, which are specific types of parallelograms) have congruent opposite sides.
- Has at least one pair of consecutive angles that is supplementary:
- Rhombus, Square, Parallelogram, Isosceles Trapezoid
- Explanation: In parallelograms, opposite angles are congruent, and consecutive angles are supplementary. For an isosceles trapezoid, consecutive angles on the same side of a base are supplementary.
- Diagonals are perpendicular:
- Kite, Rhombus, Square
- Explanation: Both a kite and a rhombus (and thus squares, as a subset of rhombuses) have perpendicular diagonals.
- Diagonals bisect one another:
- Kite, Rhombus, Square, Parallelogram
- Explanation: Diagonals bisect each other in parallelograms, rhombuses, squares, and kites. In the case of a kite, diagonals also bisect at right angles.
- A quadrilateral has two congruent diagonals which bisect each other.
- Rectangle
- Explanation: A rectangle has congruent diagonals that bisect each other. This property is exclusive to rectangles and squares (a square is a type of rectangle).