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1.5 Angle Relationships. Objective: Identify special pairs of angles and perpendicular lines. CLE 3108.3.1 Use analytic geometry tools to explore geometric problems involving parallel and perpendicular lines, circles, and special points of polygons. Measure. mA = 90 mB < 90 mC > 90.

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1 5 angle relationships

1.5 Angle Relationships

Objective: Identify special pairs of angles and perpendicular lines.

CLE 3108.3.1 Use analytic geometry tools to explore geometric problems involving parallel and perpendicular lines, circles, and special points of polygons.

measure
Measure
  • mA = 90
  • mB < 90
  • mC > 90

A

B

C

angle practice
Angle Practice
  • Draw an angle of 60; Label as A
  • Copy angle using compass. Label as B
  • Bisect angle using compass.
  • Measure angle of the two bisected sections using protractor.
  • Label size of two new angles on drawing
pairs of angles
Pairs of Angles

ABC and CBD are adjacent

A

  • Adjacent Angles
  • Vertical Angles
  • Linear Pair
  • Same vertex & common side
  • Two non-adjacent angles formed by two intersecting lines
  • Adjacent angles whose non-common sides are opposite rays

C

D

B

B

A

E

AEB and DEC

AED and BEC

C

D

DEB and BEC

Are a linear pair

B

C

D

E

identify the angles
Identify the angles
  • Two Obtuse Vertical Angles
    • AEB, DEC
  • Two Acute Adjacent Angles
    • AED, BEC
  • Name two angles that form a linear pair
      • AEB, DEC

A

B

E

D

C

pairs of angles1
Pairs of Angles
  • Complementary Angles
  • Supplementary Angles
  • Two angles whose measure have a sum of 90
  • Two angles whose measures have a sum of 180 

2

1 and 2 are complementary

1

3

4

3 and 4 are supplementary

pairs of angles2
Pairs of Angles

B

  • Perpendicular Lines
    • Intersect to form 4 right angles
    • Form congruent adjacent angles
    • AB

A

calculate angle
Calculate Angle
  • 1 + 2 = 90
  • 1 = 90 - 2
  • 1 - 2 = 12
  • 1 = 12 + 2
  • 12 + 2 = 90 - 2
  • 12 + 2 x = 90 - 2 x
  • 2x = 78
  • x = 39
  • 2 = 39
  • 1 = 90 - 2 39
  • 1 = 51
  • Find the measure of two complementary angles if the difference in the two angles is 12.

1

2

slide9

To be perpendicular

2x + 5x + 6 = 90

7x = 84

x = 12

4y-2 = 90

4y = 92

y = 23

find the value of x
Find the value of X

Vertical Angles are congruent

2x + 25 = 3x – 10

35 = x

Linear Pair are supplementary

2x + 25 + y = 180

2(35) + 25 + y = 180

70 + 25 + y = 180

Y = 95

assignment
Assignment
  • Block Class
    • Page 51, 8 - 40 every 4th
  • Honors Class
    • Page 51, 20 - 44 every 4th, 50, 54,56