Properties of Trapezoids Quiz

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Questions and Answers

Which property is true for a rectangle, but not a rhombus?

Opposite sides are congruent

Opposite angles are congruent

Diagonals bisect each other

Consecutive angles are supplementary (correct)

An isosceles trapezoid has:

One pair of parallel sides and two pairs of congruent sides

Two parallel sides and four congruent sides

One pair of parallel sides and four congruent sides

Two parallel sides and two congruent non-parallel sides (correct)

Which of the following is NOT a necessary condition for a quadrilateral to be a parallelogram?

Opposite sides are congruent

Diagonals bisect each other

Consecutive angles are supplementary

All four angles are right angles (correct)

A square is a special type of:

Parallelogram Signup and view all the answers

Which of the following is a property of a rhombus that is not necessarily true for a general trapezoid?

Diagonals are perpendicular Signup and view all the answers

Which of the following is a necessary and sufficient condition for a quadrilateral to be a trapezoid?

At least one pair of opposite sides are parallel Signup and view all the answers

Which of the following statements is NOT true about an isosceles trapezoid?

The legs are perpendicular to the bases. Signup and view all the answers

If the diagonals of a quadrilateral are perpendicular and congruent, then the quadrilateral must be a:

Square Signup and view all the answers

In a kite, the line containing the ends of the kite is a:

Symmetry line Signup and view all the answers

The formula for the area of a kite is:

$rac{1}{2}(d_1)(d_2)$ Signup and view all the answers

If a quadrilateral has two pairs of congruent adjacent sides, the quadrilateral is a:

Kite Signup and view all the answers

Which of the following statements about the midline of a trapezoid is true?

The midline is the average of the lengths of the bases. Signup and view all the answers

If a quadrilateral has diagonals that are perpendicular and bisect each other, which of the following must be true?

It is a square. Signup and view all the answers

Which of the following statements about a rhombus is false?

Each diagonal separates the rhombus into two congruent right triangles. Signup and view all the answers

If a quadrilateral has exactly one pair of parallel sides, what type of quadrilateral must it be?

Trapezoid Signup and view all the answers

Which of the following statements about a rectangle is true?

Opposite angles are congruent and supplementary. Signup and view all the answers

If a quadrilateral has all sides congruent and all angles congruent, what type of quadrilateral must it be?

Square Signup and view all the answers

Which of the following statements about an isosceles trapezoid is false?

Its diagonals are congruent. Signup and view all the answers

Study Notes

Classification of Quadrilaterals

A quadrilateral is a polygon with four sides.
Quadrilaterals are classified according to the number of parallel sides they have.

General Quadrilateral

A quadrilateral with no pair of parallel sides.

Trapezoid

A quadrilateral with exactly one pair of parallel sides.
Isosceles Trapezoid: a trapezoid with congruent nonparallel sides.

Parallelogram

A quadrilateral with two pairs of parallel sides.
Rectangle: a parallelogram with four right angles.
Rhombus: a parallelogram with four equal sides.
Square: a parallelogram with four right angles and four equal sides.

Properties of Parallelograms

Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.

Conditions for a Parallelogram

If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.
If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.
If any consecutive angles are supplementary, then the quadrilateral is a parallelogram.
If the diagonals bisect each other, then the quadrilateral is a parallelogram.

Trapezoid Properties

The parallel sides of a trapezoid are called bases while the non-parallel sides are called legs.
An angle formed by a base and a leg is called a base angle.
A diagonal is a segment that joins two nonadjacent vertices of a trapezoid.
Midline (median or midsegment) = ½(Base 1 + Base 2).

Isosceles Trapezoid

A trapezoid with two pairs of its angles congruent.
Base angles of an isosceles trapezoid are congruent.
Opposite angles of an isosceles trapezoid are supplementary.
Diagonals of an isosceles trapezoid are congruent.

Kite

A quadrilateral with two pairs of adjacent sides congruent and no opposite sides are congruent.
The common vertices of the congruent sides of the kite are called the ends of the kite.
The line containing the ends of the kite is a symmetry line for the kite.
Diagonals of a kite are perpendicular.
Area of a kite = ½(D1)(D2).
It has one pair of opposite angles congruent.
It has one diagonal that forms two isosceles triangles.

Special Parallelograms

Rectangle, rhombus, and square are quadrilaterals that are parallelograms.
Characteristics of Rectangle:
- Opposite sides are parallel and congruent.
- Opposite angles are congruent and supplementary.
- All four angles are right angles.
- Consecutive angles are supplementary.
- Diagonals bisect each other and are congruent.
- Each diagonal separates the rectangle into two congruent triangles.
Characteristics of Rhombus:
- All four sides are congruent.
- Opposite sides are parallel.
- Opposite angles are congruent.
- Consecutive angles are supplementary.
- Diagonals bisect each other and are perpendicular.
- Each diagonal bisects a pair of opposite angles.
- Each diagonal separates the rhombus into two congruent triangles.
Characteristics of Square:
- All four sides are congruent.
- All angles are right angles.
- Opposite sides are parallel and congruent.
- Opposite angles are congruent and supplementary.
- Consecutive angles are supplementary and congruent.
- Diagonals bisect each other and are perpendicular and congruent.
- Each diagonal separates the square into two congruent triangles.

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Description

Test your knowledge on the properties of trapezoids including bases, legs, base angles, diagonals, median, midsegment, and isosceles trapezoids. Learn about the relationships between the different components of a trapezoid.