unit 3: parallel and perpendicular lines section 1: lines...

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Unit 3: Parallel and Perpendicular Lines Section 1: Lines and Angles

Ex #1: Identify each of the following: A. a pair of parallel segments B. a pair of skew segments C. a pair of perpendicular segments D. a pair of parallel planes

You Try #1 Identify each of the following: A. a pair of parallel segments B. a pair of skew segments C. a pair of perpendicular segments D. a pair of parallel planes

D

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Ex #2: Give an example of each angle pair. A. corresponding angles B. alternate interior angles C. alternate exterior angles D. same-side interior angles

You Try #2: Give an example of each angle pair. A. corresponding angles B. alternate interior angles C. alternate exterior angles D. same-side interior angles

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Helpful Hint:

To determine which line is the transversal for a given angle pair, locate the line that connects the vertices.

Ex #3: Identify the transversal and classify each angle pair. A. ∠1 and ∠3 B. ∠2 and ∠6 C. ∠4 and ∠6 D. ∠2 and ∠5

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Unit 3: Parallel and Perpendicular Lines Section 2: Angles Formed by Parallel Lines and Transversals

Parallel Lines and Angle Pairs If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary.

Ex #1 Find each angle measure. A. m∠ECF

B. m∠DCE

You Try #1

Find the value x and m∠QRS.

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Ex #2 Find each angle measure. A. The value of x. B. m∠EDG You Try #2 Find m∠ABD. Ex #3 Find x and y in the diagram. Lesson Quiz State the theorem or postulate that is related to the measures of the angles in each pair. Then find the unknown angle measures. 1. m∠1 = 120°, m∠2 = (60x)° 2. m∠2 = (75x – 30)°, m∠3 = (30x + 60)° 3. m∠3 = (50x + 20)°, m∠4= (100x – 80)° 4. m∠3 = (45x + 30)°, m∠5 = (25x + 10)°

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Unit 3: Parallel and Perpendicular Lines Section 3: Proving Lines Parallel

Ex #1a Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. ∠4 ≅ ∠8 Ex #1b Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. m∠3 = (4x – 80)°, m∠7 = (3x – 50)°, x = 30 You Try #1a Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. m∠1 = m∠3

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You Try #1b Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m. m∠7 = (4x + 25)°, m∠5 = (5x + 12)°, x = 13

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Ex #2a Use the given information and the theorems you have learned to show that r || s. ∠4 ≅ ∠8 Ex #2b Use the given information and the theorems you have learned to show that r || s. m∠2 = (10x + 8)°, m∠3 = (25x – 3)°, x = 5 You Try #2a Refer to the diagram. Use the given information and the theorems you have learned to show that r || s. m∠2 = m∠6     You Try #2b Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.

m∠3 = 2x°, m∠7 = (x + 50)°, x = 50

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Ex #3 Given: p || r , ∠1 ≅ ∠3  Prove: ℓ || m You Try #3 Given: ∠1 ≅ ∠4, ∠3 and ∠4 are supplementary. Prove: ℓ || m

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Unit 3: Parallel and Perpendicular Lines Section 4: Perpendicular Lines

The ____________________________ of a segment is a line perpendicular to a segment at the segment’s midpoint. The shortest segment from a point to a line is perpendicular to the line. Ex #1: Distance From a Point to a Line A. Name the shortest segment from point A to BC. B. Write and solve an inequality for x.

You Try #1            A. Name the shortest segment from point A to BC.   B. Write and solve an inequality for x.

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Ex #2: Proving Properties of Lines Write a two-column proof. Given: r || s, ∠1 ≅ ∠2 Prove: r ⊥ t

You Try #2

Write a two-column proof. Given: ∠EHF ≅ ∠HFG , FG

⊥ GH

Prove: EH

⊥ GH

You Try #3 Solve to find x and y in the diagram.

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Unit 3: Parallel and Perpendicular Lines Section 5: Slopes of Lines

What is slope:

Determine the slope of each line.

Use the slope formula to determine the slope of JK through J(3, 1) and K(2, –1).

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Justin is driving from home to his college dormitory. At 4:00 p.m., he is 260 miles from home. At 7:00 p.m., he is 455 miles from home. Use the graph of the line that represents Justin’s distance from home at a given time. Find and interpret the slope of the line.

What if…? Use the graph below to estimate how far Tony will have traveled by 6:30 P.M. if his average speed stays the same.

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Slopes of Parallel and Perpendicular Lines

Graph each pair of lines. Use their slopes to determine whether they are parallel, perpendicular, or neither.

UV

and XY

U(0, 2), V(–1, –1), X(3, 1), Y(–3, 3)

GH

and IJ

G(–3, –2), H(1, 2), I(–2, 4), J(2, –4)

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CD

and EF

C(–1, –3), D(1, 1), E(–1, 1), F(0, 3)