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

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 11-1 Slides

Arrangements of two lines Parallel Intersect at A MA202 Sections 5 & 401 Chapter 11-1 Slides

Arrangements of three lines All 3 Parallel Concurrent, intersecting at B MA202 Sections 5 & 401 Chapter 11-1 Slides

Arrangements of three lines (cont) 2 parallel and a transversal Intersect at 3 points (general position) MA202 Sections 5 & 401 Chapter 11-1 Slides

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

Rays, Angles and Angle Measure Ray − → Interior and Exterior PQ ∠ BAC of an angle Note: m ( ∠ BAC ) is the measure of ∠ BAC . MA202 Sections 5 & 401 Chapter 11-1 Slides

Types of angles Zero angle Acute angle Right angle MA202 Sections 5 & 401 Chapter 11-1 Slides

Types of angles (cont) Obtuse angle Straight angle Reflex angle MA202 Sections 5 & 401 Chapter 11-1 Slides

Perpendicular Perpendicular lines Perpendicular segments MA202 Sections 5 & 401 Chapter 11-1 Slides

Congruent angles ∠ P ∼ = ∠ Q MA202 Sections 5 & 401 Chapter 11-1 Slides

Complementary angles MA202 Sections 5 & 401 Chapter 11-1 Slides

Supplementary angles MA202 Sections 5 & 401 Chapter 11-1 Slides

Adjacent angles MA202 Sections 5 & 401 Chapter 11-1 Slides

Vertical angles ∠ 1 and ∠ 3 are vertical angles. ∠ 2 and ∠ 4 are vertical angles. MA202 Sections 5 & 401 Chapter 11-1 Slides

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

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

Example 11.3 (a) Find the measure of each angle. MA202 Sections 5 & 401 Chapter 11-1 Slides

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

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

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

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

Example 11.4 Show m ( ∠ 1) + m ( ∠ 2) = m ( ∠ 4). MA202 Sections 5 & 401 Chapter 11-1 Slides

Example 11.5 The altitudes in a triangle are concurrent. MA202 Sections 5 & 401 Chapter 11-1 Slides

Directed angles MA202 Sections 5 & 401 Chapter 11-1 Slides

Example 11.6 MA202 Sections 5 & 401 Chapter 11-1 Slides