Download Similar Triangles - Lesson 18(3)

Similar is a mathematical word meaning the same
shape.
We say that two triangles , triangle FDE and
triangle LMK, are similar if the ratio of each side is
similar.
FD : DE : EF = LM : MK : KL
This equation of two three term ratios can also be
written in fraction form:
FD DE EF
=
=
LM MK KL
NOTE:
All sides of one triangle must
be either all in the numerator
or denominator.
Corresponding sides are equal
In similar triangles, corresponding angles are
equal.
F =  L
D=M
E=K
IMPORTANT:
If you know two triangles are similar, then their
corresponding angles are equal.
Conversely, if two triangles have equal
corresponding angles, then the triangles are
similar.
Prove the two triangles are similar?
SOLUTION:
Angles:
K =  A
L=B
M=C
Sides:
KL
KM
LM
=
=
AB
AC
BC
8
10
6
=
=
12
15
9
1080 1080 1080
=
=
1620 1620 1620
Since corresponding angles are
equal, then corresponding sides are
equal. Therefore the two triangles
are similar.
Prove the two triangles are similar?
SOLUTION:
Angles:
Sides:
Prove the two triangles are similar?
SOLUTION:
Angles:
L =  K
M=S
O=T
Sides:
LM
LO
=
KS
KT
4
5
=
=
MO
ST
5
6
=
6.25
7.5
187.5
187.5
187.5
=
=
234.38
234.38
234.38
Since corresponding angles are
equal, then corresponding sides are
equal. Therefore the two triangles
are similar.
Solve for the unknown values.
SOLUTION:
Sides:
Angles:
AB
BC
AC
=
=
DE
DC
EC
A=  E
B=D
3
9
C= C
3
9
=
4
y
=
4
y
=
x
12
3
x
=
9
12
9(4) = 3y
3(12) = 9x
36 = 3y
36 = 9x
12 = y
4=x
Solve for the unknown values.
SOLUTION:
Angles:
Sides:
Solve for the unknown values.
SOLUTION:
Sides:
Angles:
CT
TZ
=
PR
RZ
C=  P
T=R
6
9
Z= Z
6
9
=
3
y
=
3
y
=
CZ
PZ
=
x
12
6
x
=
9
12
9(3) = 6y
6(12) = 9x
27 = 6y
72 = 9x
4.5 = y
8=x
Class work
• Copy down examples
• Finish Lesson 18(2) worksheet.