# Download Section 1.2 Angle Relationships and Similar Triangles

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```Do Now
Find the supplement of each angle.
1.83°
2.35°
3.165°
4.73°
5.124°
Copyright © 2005 Pearson Education, Inc.
Slide 1-1
Section 1.2
Angle Relationships and Similar
Triangles
Objective:
SWBAT use geometric properties to identify similar triangles
and angle relationships.
Copyright © 2005 Pearson Education, Inc.
Vertical Angles
Vertical Angles have equal measures.
Q
R
M
N
P
The pair of angles NMP and RMQ are vertical
angles.
Do you see another pair of vertical angles?
Copyright © 2005 Pearson Education, Inc.
Slide 1-3
Parallel Lines
Parallel lines are lines that lie in the same plane
and do not intersect.
When a line q intersects two parallel lines, q, is
called a transversal. Eight angles are now
formed.
Transversal
q
m
parallel lines
n
Copyright © 2005 Pearson Education, Inc.
Slide 1-4
Angles and Relationships
q
m
n
Name
Angles
Rule
Alternate interior angles
4 and 5
3 and 6
Angles measures are equal.
Alternate exterior angles
1 and 8
2 and 7
Angle measures are equal.
Interior angles on the same
side of the transversal
4 and 6
3 and 5
Angle measures add to 180.
Corresponding angles
2 & 6, 1 & 5,
3 & 7, 4 & 8
Angle measures are equal.
Copyright © 2005 Pearson Education, Inc.
Slide 1-5
Finding Angle Measures
Find the measure of each
marked angle, given that
lines m and n are parallel.
(6x + 4)
(10x  80)
m
n
The marked angles are
alternate exterior angles,
which are equal.
Copyright © 2005 Pearson Education, Inc.
6 x  4  10 x  80
84  4 x
21  x
One angle has measure
6x + 4 = 6(21) + 4 = 130
and the other has measure
10x  80 = 10(21)  80 = 130
Slide 1-6
Finding Angle Measures
B
m<A = 58°
C
D
Z
W
Y
X
Copyright © 2005 Pearson Education, Inc.
Slide 1-7
Angle Sum of a Triangle
Take your given triangle.
Tear each corner from the triangle. (so you now have 3 pieces)
Rearrange the pieces so that the 3 pieces form a straight angle.
Convincing?!?
The sum of the measures of the angles of any
triangle is 180.
Copyright © 2005 Pearson Education, Inc.
Slide 1-8
Applying the Angle Sum
The measures of two of the
angles of a triangle are 52
and 65. Find the measure
of the third angle, x.
Solution
52  65  x  180
117  x  180
x  63
65
x
52
Copyright © 2005 Pearson Education, Inc.
Slide 1-9
Applying the Angle Sum
The measures of two of the
angles of a triangle are 48
and 61. Find the measure
of the third angle, x.
Solution:
48
x
61
Copyright © 2005 Pearson Education, Inc.
Slide 1-10
Types of Triangles: Angles
Copyright © 2005 Pearson Education, Inc.
Slide 1-11
Types of Triangles: Sides
Copyright © 2005 Pearson Education, Inc.
Slide 1-12
Homework
Page 14-16
# 4, 6, 12, 13, 16, 18, 26, 30, 34
Copyright © 2005 Pearson Education, Inc.
Slide 1-13
Do Now
Find the measures of all the angles.
(2x – 21)°
Copyright © 2005 Pearson Education, Inc.
(5x – 129)°
Slide 1-14
Section 1.2…Day 2
Angle Relationships and Similar
Triangles
Objective:
SWBAT use geometric properties to identify similar triangles
and angle relationships.
Copyright © 2005 Pearson Education, Inc.
Conditions for Similar Triangles
Similar Triangles are triangles of exactly the same
shape but not necessarily the same size.
Corresponding angles must have the same
measure.
Corresponding sides must be proportional.
(That is, their ratios must be equal.)
Copyright © 2005 Pearson Education, Inc.
Slide 1-16
Finding Angle Measures
Triangles ABC and DEF
are similar. Find the
measures of angles D and
E.


D
Since the triangles are
similar, corresponding
angles have the same
measure.
Angle D corresponds to
angle A which = 35
A
112
35
F
C
112
33
Copyright © 2005 Pearson Education, Inc.
E

Angle E corresponds to
angle B which = 33
B
Slide 1-17
Finding Side Lengths
Triangles ABC and DEF are
similar. Find the lengths of
the unknown sides in
triangle DEF.

32 64

16
x
32 x  1024
x  32
D
A

16
112
35
64
F
32
C
112
33
48
Copyright © 2005 Pearson Education, Inc.
To find side DE.
B
E
To find side FE.
32 48

16 x
32 x  768
x  24
Slide 1-18
Application

A lighthouse casts a
shadow 64 m long. At the
same time, the shadow
cast by a mailbox 3 feet
high is 4 m long. Find the
height of the lighthouse.

The two triangles are
similar, so corresponding
sides are in proportion.
3 x

4 64
4 x  192
x  48
3

4
x
The lighthouse is 48 m
high.
64
Copyright © 2005 Pearson Education, Inc.
Slide 1-19
Homework
Page 17-18
# 42-56 (evens)
Copyright © 2005 Pearson Education, Inc.
Slide 1-20
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