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Classifying Quadrilaterals

Properties of Parallelograms

Rectangles Rhombii Trapezoids and Kites

Classify the following diagram in as many ways as possible.

Quadrilateral

Parallelogram

Rhombus

Name the quadrilateral that has two pairs of adjacent

sides that are congruent and no opposite sides congruent.

Kite

What is the difference between a trapezoid and an isosceles trapezoid?

A trapezoid is a quadrilateral with exactly one pair of parallel sides.

An isosceles trapezoid is a trapezoid whose nonparallel opposite sides are congruent.

Find the value of x and y and then find the length of each side of the

rhombus below.

x = 3

y = 5

All sides lengths are 15

Complete the following diagram representing the relationships among special quadrilaterals.

Opposite sides of a parallelogram are _________________

Congruent

Explain why consecutive angles in a parallelogram are

supplementary.

Consecutive angles are formed by two parallel lines cut by a transversal. These angle pairs are classified as same-side interior angles and same-side interior angles are supplementary when two

parallel lines are cut by a transversal.

Based on the markings, decide whether each figure must be a

parallelogram.a. b.

a. Yes; both pairs of alternate interior angles are congruent, therefore both pairs of opposite sides are parallel.

b. No; the diagonals do not necessarily bisect each other.

Find the values of x and y for the parallelogram below.

x = 30

y = 55

Find the values of x and y and then find the length of each diagonal for

the parallelogram below.

x = 8

y = 25

50; 80

Fill in the blank with always, sometimes, or never.

A rectangle is ___________ a square.

Sometimes

What is the relationship between the diagonals of a rectangle?

They are congruent

True or False?

a. The opposite sides of a rectangle are congruent.

b. The diagonals of a rectangle are always perpendicular.

c. The diagonals of a rectangle bisect each other.

d. The opposite angles of a rectangle are both congruent and supplementary.

a. True; a rectangle is a parallelogram and the opposite sides of a parallelogram are congruent

b. False; unless the rectangle is a square, the diagonals are not perpendicular.

c. True; a rectangle is a parallelogram and the diagonals of a parallelogram bisect each other.

d. True; all four angles in a rectangle are 90 degrees, therefore the opposite angles are both congruent and supplementary.

Determine if the following diagrams are rectangles. Justify your answer.

a. b.

a. No; the diagonals are not necessarily congruent.

b. Yes; the diagonals are congruent.

Find the value of x for the following rectangle and then find

the length of each diagonal.

3RZ x 5SW x

x = 11

AC = BD = 16

What are the characteristics of a

rhombus?

A rhombus is a parallelogram with all four

sides congruent.

True or False?

A square is a rhombus.

True

Based on the following diagram, determine if the

parallelogram is a rhombus.

Yes; the diagonal is bisecting two angles.

Find the missing angle measures for the rhombus below.

90; 60; 60; 30

Find the value of x for which ABCD is a rhombus.

x = 4/3

y = 7

Find the value of x for the isosceles trapezoid below.

x = 3

Find the measure of each angle for the isosceles trapezoid below.

Justify your answer.

1 = 62; base angles of an isosceles trapezoid are congruent.

2 = 118; angle 2 and the 62 degree angle are s.s.-interior angles.

3 = 118; angles 2 and 3 are base angles.

Find the value of x for the isosceles trapezoid below.

x = 4

Find the value of each missing angle for the kite below.

90; 9; 81; 40

Find the values of x and y for the kite below.

x = 35

y = 30