Transcript 11.5 Similar Triangles

11.5 Similar Triangles
Identifying Corresponding Sides of
Similar Triangles
By: Shaunta Gibson
Similar Triangles
are triangles that have the same
shape but not necessarily the same size.
B
E
A
C
D
F
In the diagram above, triangle ABC is equal to triangle DEF. We write
it as ABC ~ DEF. In the diagram, each angle of ABC corresponds to
an angle of DEF as follows:
Similar Triangles
are triangles that have the same
shape but not necessarily the same size.
B
E
C
A
angle A = angle D
angle B = angle E
D
angle C = angle F
Also, each side of ABC corresponds to a side of DEF
AB corresponds to DE
BC corresponds to EF AC corresponds to DF
F
In similar triangles, corresponding
sides opposite the equal angles.
*
sides are the
When we write that two angles are similar, we name them so
that the order of corresponding angles in both triangles is the
same.
B
triangle ABC ~ triangle DEF
E
A
C
D
F
Triangle RST ~ triangle XYZ. Name the
corresponding sides of these triangles.
T
S
Z
R
X
Because RST ~ XYZ that means angle R = angle X, angle S =
angle Y, and angle T = angle Z.
Now we write the following:
Angle R = Angle X, so ST corresponds to YZ.
Angle S = Angle Y, so RT corresponds to XZ.
Angle T = Angle Z, so RS corresponds to XY.
Y
In similar triangles, corresponding sides are in
proportion: that is, the ratios of their length are equal. As
shown below in the example triangle ABC ~ DEF,
therefore we have the following
AB
DE
BC
EF
B
AC
DF
8 cm
6 cm
6
3
8
4
4
2
18
9
A
C
4 cm
E
2
1
3 cm
4 cm
D
F
2 cm
Finding the Missing Sides of Similar Triangles
•
To find a missing side of similar triangles
1.)
write the ratios of the lengths of the corresponding
sides
2.) write a proportion using a ratio with known terms
and a ratio with an unknown term
3.) solve the proportion for the unknown term
In the following diagram, triangle TAP ~
triangle RUN. Find x.
Because TAP ~ RUN, we write the ratios of the lengths of the
corresponding sides.
A
15 cm
T
N
x
P
30 cm
15
x
9
12
12 cm
9 cm
or
R
18 cm
x
30
12
18
U
Now cross multiply, then divide to get
the length of AP.
A
15 cm
T
N
x
P
30 cm
15
x
9
12
12 cm
9 cm
R
18 cm
9x = 180: x = 20
so x, or the length of AP, is 20 cm
U
THANK YOU
T
E
E
H
N
D