5.12 Quadrilaterals

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpIdentify the triangle based on the given measurements.

1. 3 ft, 4 ft, 6 ft

2. 46°, 90°, 44°

3. 7 in., 7 in., 10 in.

scalene

right

isosceles

Course 2

7-7 Quadrilaterals

Problem of the Day

One angle of a parallelogram measures 90°. What are the measures of the other angles?all 90°

Course 2

7-7 Quadrilaterals

Learn to name and identify types of quadrilaterals.

Course 2

7-7 Quadrilaterals

Vocabulary

parallelogramrhombusrectanglesquaretrapezoidkite

Insert Lesson Title Here

Course 2

7-7 Quadrilaterals

Course 2

7-7 Quadrilaterals

Some quadrilaterals have properties that classify them as special quadrilaterals. Here are six major special quadrilaterals.

A parallelogram has two pairs of parallel sides.

Course 2

7-7 Quadrilaterals

Some quadrilaterals have properties that classify them as special quadrilaterals. Here are six major special quadrilaterals.

A rhombus has four congruent sides.

Course 2

7-7 Quadrilaterals

Some quadrilaterals have properties that classify them as special quadrilaterals. Here are six major special quadrilaterals.

A rectangle has four right angles.

Course 2

7-7 Quadrilaterals

Some quadrilaterals have properties that classify them as special quadrilaterals. Here are six major special quadrilaterals.

A square has four congruent sidesand four right angles.

Course 2

7-7 Quadrilaterals

Some quadrilaterals have properties that classify them as special quadrilaterals. Here are six major special quadrilaterals.

A trapezoid has exactly one pairof parallel sides.

Course 2

7-7 Quadrilaterals

Some quadrilaterals have properties that classify them as special quadrilaterals. Here are six major special quadrilaterals.

A kite has exactly two pairs of congruent adjacent sides.

Course 2

7-7 Quadrilaterals

Quadrilaterals can have more than onename because the special quadrilateralssometimes share properties.

Give all the names that apply to the quadrilateral.

Additional Example 1A: Identifying Types of Quadrilaterals

Course 2

7-7 Quadrilaterals

This figure has two pairs of parallel sides, so it is a parallelogram.

It has four congruent sides, so it is also a rhombus.

Give all the names that apply to the quadrilateral.

Additional Example 1B: Identifying Types of Quadrilaterals

Course 2

7-7 Quadrilaterals

The figure has exactly two pairs of congruent, adjacent sides, so it is a kite.

It does not fit the definitions of any of the other special quadrilaterals.

Give all the names that apply to the quadrilateral.

Additional Example 1C: Identifying Types of Quadrilaterals

Course 2

7-7 Quadrilaterals

The figure has two pairs of parallel sides, so it is a parallelogram.

It has four right angles, so it is also a rectangle.

Give all the names that apply to the quadrilateral.

Try This: Example 1A

Course 2

7-7 Quadrilaterals

This figure has two pairs of parallel sides, so it is called a parallelogram.

It has four right angles, so it is also a rectangle.

Give all the names that apply to the quadrilateral.

Try This: Example 1B

Course 2

7-7 Quadrilaterals

The figure has two pairs of parallel sides, so it is a parallelogram.

6 ft6 ft

6 ft 6 ft It has four congruent sides, so it is also a rhombus.

Give all the names that apply to the quadrilateral.

Try This: Example 1C

Course 2

7-7 Quadrilaterals

The figure has exactly one pair of parallel sides, so it is a trapezoid.

It does not fit the definitions of any of the other special quadrilaterals.

Tell whether the statement is true or false. Explain your answer.

Additional Example 2A: Recognizing Relationships Between Quadrilaterals

Course 2

7-7 Quadrilaterals

A. All rhombuses are squares.

A rhombus has four congruent sides, but some may or may not have right angles. The statement is false.

Tell whether the statement is true or false. Explain your answer.

Additional Example 2B: Recognizing Relationships Between Quadrilaterals

Course 2

7-7 Quadrilaterals

B. Not all squares are rectangles.

A square has four right angles. A rectangle also has four right angles. So a square is a rectangle. The statement is false.

Tell whether the statement is true or false. Explain your answer.

Additional Example 2C: Recognizing Relationships Between Quadrilaterals

Course 2

7-7 Quadrilaterals

C. Some parallelograms are squares.

A square has all the properties of a parallelogram, so some parallelograms do have equal sides and right angles; however, some do not. The statement is true.

Tell whether the statement is true or false. Explain your answer.

Try This: Example 2A

Course 2

7-7 Quadrilaterals

A. All squares are rectangles.

A square has four right angles. A rectangle also has four right angles. So a square is a rectangle. The statement is true.

Tell whether the statement is true or false. Explain your answer.

Try This: Example 2B

Course 2

7-7 Quadrilaterals

B. Some rectangles are squares.

If the rectangle has four congruent sides, then it is a square. The statement is true.

Tell whether the statement is true or false. Explain your answer.

Try This: Example 2C

Course 2

7-7 Quadrilaterals

C. Some trapezoids are squares.

A square has two sets of parallel sides, but a trapezoid has only one set of parallel sides. The statement is false.

Lesson Quiz: Part 1

Insert Lesson Title Here

Course 2

7-7 Quadrilaterals

1. Give all the names that apply to the quadrilateral.

rhombusquadrilateralparallelogram

Identify the quadrilateral described.

2. 4 right angles, 4 congruent sidessquare

3. only one pair of parallel sidestrapezoid

Lesson Quiz: Part 2

Insert Lesson Title Here

Course 2

7-7 Quadrilaterals

Tell if each statement is true or false. Explain.

4. All quadrilaterals are parallelograms.

False; a quadrilateral is any 4-sided polygon.

5. Every parallelogram is a rectangle.

False; a rectangle is a specific kind of parallelogram with four right angles.