1.6 Angle Relationships 9/10/12

• Pairs of Angles– Adjacent Angles– Vertical Angles– Linear Pair– Complementary– Supplementary

CCSS: G-CO1Know precise definitions of Know precise definitions of angleangle, circle, , circle, perpendicular line, perpendicular line, parallel line, and line segment,parallel line, and line segment, based on the undefined notions based on the undefined notions of of point, line, distance along a point, line, distance along a lineline, and distance around a , and distance around a circular arc.circular arc.

Mathematical Practice

1. Make sense of problems, and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments, and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for, and make use of, structure.

8. Look for, and express regularity in, repeated reasoning.

E.Q:

• 1. What are characteristics of complementary, supplementary, adjacent, linear and vertical angles?

• 2. How do we use the formulas for area and perimeter of 2-D shapes to solve real life situations?

Adjacent Angles• Adjacent angles – two angles that lie in the same

plane, have a common vertex, and share a common side, but NO common interior points.

A

B

C

D

A

B

C

D

ABC and CBD

Vertical Angles• Vertical angles – two nonadjacent angles

formed by two intersecting lines.

A B

DC

E

AEBand CED AEDand BEC

Linear Pair• A linear pair – a pair of adjacent angles whose

non-common sides are opposite rays.

B

D C E

BEDand BEC

Identify Angle Pairs• Name an angle pair that satisfies each condition.

a. Two obtuse vertical angles.

b. Two acute adjacent angles.

YT W

V

Z

X

115°

65° 65°

65°50°

VZXand YZW VZYand YZT

YZTand TZW TZWand WZX

Angle Relationships• Complementary Angles

– Two angles whose measures have a sum of 90°.

12

A

C

B

D F

50°

E

40°

1 2and ABCand DEF

Angle Relationships• Supplementary Angles

– Two angles whose measures have a sum of 180°.A

D

B C

Mand N

ABDand CBD

MN

80°100°

Angle Measures• Find the measure of two complementary angles if the

difference of the measures is 12.

A B

x°

Angle Measures• Find the measure of two complementary angles if the

difference of the measures is 12.

12m B m A (90 ) 12x x 90 2 12x 2 78x

39x 39m A 90 39m B

51

Perpendicular Lines• Perpendicular lines – lines that form right angles

– Intersect to form four right angles.– Intersect to form congruent adjacent angles.– Segments and rays can be perpendicular to lines or to the

other line segments and rays.– The right angle symbol in the figure indicates that the lines

are perpendicular.

• is read “is perpendicular to”.

• XZ WYX Z

Y

W

Perpendicular Lines• Find x and y so that BE and AD are perpendicular.m BFD m BFC CFD 90 6 3x x 90 9x10 x

12 10m AFE y 90 12 10y 100 12 y25

3y

A D

B

E

F

C

6x°3x°

(12y – 10)°

1.7 Introduction to Perimeter, 1.7 Introduction to Perimeter, Circumference, & AreaCircumference, & Area

9/10/129/10/12

RectangleRectangle

• Perimeter

P=2l +2w

• Area

A=lw

l

(length)

W

(width)

SquareSquare

• Perimeter

P=4s

• Area

A=s2

S

(side)

Example: Find the perim. & area of the figure.Example: Find the perim. & area of the figure.

• P=2l +2w P=2(5in)+2(3in)

P=10in+6in

P=16in

• A=lw A=(5in)(3in)

A=15in2

3 in

5 in

Ex: Find the perim. & area of the figure.Ex: Find the perim. & area of the figure.

• P=4s

P=4(20m)

P=80m

• A=s2

A=(20m)2

A=400m2

20 m

TriangleTriangle

• Perimeter

P=a+b+c

• Area

A= ½ bh

b

(base)

h

(height)

a c

Ex: Find the perim. & area of the figure.Ex: Find the perim. & area of the figure.• P=a+b+c

P=5ft+7ft+6ft

P=18 ft

• A= ½ bh

A= ½ (7ft)(4ft)

A= ½ (28ft2)

A= 14ft2

7 ft7 ft

5 ft5 ft

4 ft4 ft

6 ft6 ft

CircleCircle• Diameter

d=2r

• Circumference

C=2πr

• Area

A=πr2

diameterradius

** Always use the ** Always use the ππ button on the calculator; button on the calculator; even when the directions say to use 3.14.even when the directions say to use 3.14.

Ex: Find the circumference & area of the Ex: Find the circumference & area of the circle.circle.

• C=2πr

C=2π(5in)

C=10π in

C≈31.4 in

• A=πr2

A=π(5in)2

A=25π in2

A≈78.5 in2

10in

10in

GROUP WORKGROUP WORKCHAMPs #2CHAMPs #2