Transparency 4

Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.

Objective

Find missing angle measures in quadrilaterals and classify

quadrilaterals

Vocabulary

Quadrilateral

A polygon that has four sides and four angles and the total of the four angles is 3600

Vocabulary

Trapezoid

A quadrilateral with exactly one pair of parallel opposite sides

Vocabulary

Parallelogram

A quadrilateral with both pairs of opposite sides parallel and congruent

Vocabulary

Rectangle

A parallelogram with four right angles

Vocabulary

Rhombus

A parallelogram with four congruent sides but does not have 900 angles

Vocabulary

Square

A parallelogram with four congruent sides and four right angles

Example 1 Find a Missing Angle Measure

Example 2 Classify Quadrilaterals

Example 3 Classify Quadrilaterals

Find the value of q in quadrilateral PQRS.

1/3

Definition of quadrilateral states that the sum of the angles is 3600

Write equation for sum of angles of the quadrilateral

mP + mS + mR + mQ = 360

Group the known values together

Find the value of q in quadrilateral PQRS.

1/3

Replace mP with 124

mP + mS + mR + mQ = 360

124

Replace mS with 120

124 + 120

Replace mR with 36

124 + 120 + 36

Define the variable q as the unknown (can use m Q)

124 + 120 + 36 + q

Find the value of q in quadrilateral PQRS.

1/3

Bring down = 360

mP + mS + mR + mQ = 360

124124 + 120124 + 120 + 36124 + 120 + 36 + q124 + 120 + 36 + q = 360

Combine “like” terms

280 + q = 360

Ask “what is being done to the variable?”

The variable is being added by 280

Find the value of q in quadrilateral PQRS.

1/3

Do the inverse on both sides of the equal sign

mP + mS + mR + mQ = 360

124124 + 120124 + 120 + 36124 + 120 + 36 + q124 + 120 + 36 + q = 360

280 + q = 360

Bring down 280

280

Subtract 280

280 - 280

Bring down + q = 360

280 - 280 + q = 360

Find the value of q in quadrilateral PQRS.

1/3

Subtract 280

mP + mS + mR + mQ = 360

124124 + 120124 + 120 + 36124 + 120 + 36 + q124 + 120 + 36 + q = 360

280 + q = 360

280 280 - 280 280 - 280 + q = 360 280 - 280 + q = 360 - 280

Combine “like” terms0

Bring down + q =

0 + q =

Combine “like” terms

0 + q = 80

Find the value of q in quadrilateral PQRS.

1/3

Use the Identity Property to add 0 + q

mP + mS + mR + mQ = 360

124124 + 120124 + 120 + 36124 + 120 + 36 + q124 + 120 + 36 + q = 360

280 + q = 360

280 280 - 280 280 - 280 + q = 360 280 - 280 + q = 360 - 280

0 0 + q = 0 + q = 80 q = 80 Add dimensional analysisq = 800

Answer: mQ =800

Answer: 1500

Find the value of q in quadrilateral QUAD.

1/3

Answer: quadrilateral

Classify the quadrilateral using the name that best describes it.

No congruent sides

2/3

No special angles

Answer: rhombus

Classify the quadrilateral using the name that best describes it.

2/3

All sides are congruent

2 pair of sides parallel

Answer: square

Classify the quadrilateral using the name that best describes it.

3/3

All sides are congruent

All angles are right (900)

Answer: rectangle

Classify the quadrilateral using the name that best describes it.

*

3/3

Opposite sides congruent and parallel

All angles are right (900)

Assignment

Lesson 6:4 Classifying Quadrilaterals 4 - 23 All