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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Answer: quadrilateral

Classify the quadrilateral using the name that best describes it.

No congruent sides

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No special angles

Answer: rhombus

Classify the quadrilateral using the name that best describes it.

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All sides are congruent

2 pair of sides parallel

Answer: square

Classify the quadrilateral using the name that best describes it.

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All sides are congruent

All angles are right (900)

Answer: rectangle

Classify the quadrilateral using the name that best describes it.

*

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Opposite sides congruent and parallel

All angles are right (900)

Assignment

Lesson 6:4 Classifying Quadrilaterals 4 - 23 All