Points Points A , B , P and Q . MA202 Sections 5 & 401 Chapter - - PowerPoint PPT Presentation

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Points Points A , B , P and Q . MA202 Sections 5 & 401 Chapter - - PowerPoint PPT Presentation

Jan 28, 2023 377 likes •674 views

Points Points A , B , P and Q . MA202 Sections 5 & 401 Chapter 11-1 Slides Lines Lines AB and l . MA202 Sections 5 & 401 Chapter 11-1 Slides Collinear Noncollinear points Collinear points MA202 Sections 5 & 401 Chapter

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SLIDE 1

Points

Points A, B, P and Q.

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 2

Lines

Lines ← → AB and l.

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 3

Collinear

Noncollinear points Collinear points

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 4

Arrangements of two lines

Parallel Intersect at A

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 5

Arrangements of three lines

All 3 Parallel Concurrent, intersecting at B

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 6

Arrangements of three lines (cont)

2 parallel and a transversal Intersect at 3 points (general position)

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 7

Segments, length and congruence

Segment AB AB ∼ = CD M is the midpoint of AB Note: AB is the length of AB.

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 8

Rays, Angles and Angle Measure

Ray − → PQ ∠BAC Interior and Exterior

f an angle

Note: m(∠BAC) is the measure of ∠BAC.

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 9

Types of angles

Zero angle Acute angle Right angle

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 10

Types of angles (cont)

Obtuse angle Straight angle Reflex angle

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 11

Perpendicular

Perpendicular lines Perpendicular segments

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 12

Congruent angles

∠P ∼ = ∠Q

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 13

Complementary angles

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 14

Supplementary angles

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 15

Adjacent angles

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 16

Vertical angles

∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 17

Corresponding angles

∠1 and ∠5 are corresponding angles. ∠2 and ∠6 are corresponding angles. ∠3 and ∠7 are corresponding angles. ∠4 and ∠8 are corresponding angles.

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 18

Corresponding-Angles Property

∠1 and ∠5 are corresponding angles. ∠2 and ∠6 are corresponding angles. ∠3 and ∠7 are corresponding angles. ∠4 and ∠8 are corresponding angles.

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 19

Example 11.3

(a) Find the measure of each angle.

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 20

Example 11.3

(b) How can we construct a line through Q which is parallel to the blue line?

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 21

Alternate interior angles

∠3 and ∠5 are alternate interior angles. ∠4 and ∠6 are alternate interior angles.

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 22

Alternate-Interior-Angles Theorem

∠3 and ∠5 are alternate interior angles. ∠4 and ∠6 are alternate interior angles.

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 23

Sum of degrees in a triangle

How are ∠3 and ∠4 related? How are ∠2 and ∠5 related?

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 24

Example 11.4

Show m(∠1) + m(∠2) = m(∠4).

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 25

Example 11.5

The altitudes in a triangle are concurrent.

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 26

Directed angles

MA202 Sections 5 & 401 Chapter 11-1 Slides

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SLIDE 27

Example 11.6

MA202 Sections 5 & 401 Chapter 11-1 Slides