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Chapter
Chapter6
2
Ratio, Proportion,
and Triangle
Applications
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 1
Section 6.5
Congruent and
Similar Triangles
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 2
Congruent Triangles
Two triangles are congruent when they have the same
shape and the same size. Corresponding angles are
equal, and corresponding sides are equal.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 3
Angle-Side-Angle (ASA)
If the measures of two angles of a triangle equal
the measures of two angles of another triangle,
and the lengths of the sides between each pair of
angles are equal, the triangles are congruent.
For example, these two triangles are congruent by
Angle-Side-Angle.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 4
Side-Side-Side (SSS)
If the lengths of the three sides of a triangle equal
the lengths of the corresponding sides of another
triangle, the triangles are congruent.
For example, these two triangles are congruent by
Side-Side-Side.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 5
Side-Angle-Side (SAS)
If the lengths of two sides of a triangle equal the
lengths of corresponding sides of another triangle,
and the measures of the angles between each pair
of sides are equal, the triangles are congruent.
For example, these two triangles are congruent by
Side-Angle-Side.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 6
Example
Determine whether triangle MNO is congruent to
triangle RQS.
Since the lengths of all three sides of triangle
MNO equal the lengths of all three sides of
triangle RQS, the triangles are congruent.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 7
Example
Determine whether triangle GHI is congruent to
triangle JKL.
The triangles are NOT congruent. The angle
measures are not the same.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 8
Similar Triangles
Similar triangles are found in art, engineering,
architecture, biology, and chemistry. Two
triangles are similar when they have the same
shape but not necessarily the same size.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 9
Similar Triangles
In similar triangles, the measures of corresponding angles
are equal and corresponding sides are in proportion.
a=3
b=5
c=8
d=6
e = 10
f = 16
Side a corresponds to side d, side b corresponds to side e, and
side c corresponds to side f.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 10
Example
Find the ratio of corresponding sides for the
similar triangles QRS and XYZ.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 11
Example
Given that the triangles are similar, find the
missing length x.
Since the triangles are similar,
corresponding sides are in
proportion.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 12
Example
Tammy Shultz, a firefighter, needs to estimate the
height of a burning building. She estimates the
length of her shadow to be 8 feet long and the
length of the building’s shadow
to be 60 feet long. Find the
approximate height of the
building if she is 5 feet tall.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 13
Example
5 n

8 60
5  60  8  n
300  8n
300 8n

8
8
37.5  n
The height of the building is about 37.5 feet.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 14