Download Similar Triangles - Lesson 18(2)

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:
A =  D
B=E
C=F
Sides:
AB
BC
AC
=
=
DE
EF
DF
8
6
=
12
9
=
5
7.5
540 540
540
=
=
810 810
810
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:
M =  O
L=P
N=Q
Sides:
ML
MN
LN
=
=
OP
OQ
PQ
4
6
3
=
=
12
18
9
12
12
=
36
36
=
Since corresponding angles are
equal, then corresponding sides are
equal. Therefore the two triangles
are similar.
12
36
Find the measures of  A,  B,  C.
SOLUTION:
Sides:
Since the ratios of
the sides are all
equal, the
triangles are
similar, that also
means the
corresponding
angles are equal.
FH
FG
GH
=
=
AC
AB
BC
3.5
3
=
7
6
=
5.3
10.6
1
2
=
1
2
=
1
2
Therefore:  F =  A
A = 100o
H=C
 C = 38o
G=B
 B = 42o
Find the measures of  M,  L,  K.
SOLUTION:
Sides:
Find the measures of  M,  L,  K.
SOLUTION:
Sides:
Since the ratios of
the sides are all
equal, the
triangles are
similar, that also
means the
corresponding
angles are equal.
ML
MK
LK
=
=
AB
AC
BC
16
20
18
=
=
4
5
4.5
4
Therefore:  M =  A
= 4
= 4
M = 105o
L=B
 L = 17o
K=C
 K = 58o
Triangle ABC is similar to Triangle
RPQ. Find the lengths of RP and AC
SOLUTION:
Sides:
AB
BC
AC
=
=
RP
PQ
RQ
8
x
8
x
=
12
16.8
=
12
y
=
16.8
21
12
y
=
16.8
21
12x = 8(16.8)
16.8y = 12(21)
x=
y = 252
134.4
12
RP = 11.2
16.8
AC = 15
Triangle SIP is similar to Triangle
MAT. Find the lengths of MA and SP
SOLUTION:
Sides:
Triangle SIP is similar to Triangle
MAT. Find the lengths of MA and SP
SOLUTION:
Sides:
SI
SP
IP
=
=
MA
MT
AT
7
x
7
x
=
13
25
=
y
13
=
17.3
25
13
25
=
y
17.3
13x = 7(25)
25y = 13(17.3)
x=
y = 224.9
175
13
MA = 13.5
25
SP = 9
For the figure below, show that
Triangle DEF is similar to Triangle
DGH.
SOLUTION:
If two triangles have equal
corresponding angles, then the triangles
are similar.
Therefore:
D =  D ( common angle)
 E =  G (Corresponding angles)
 F =  H ( corresponding angles )
Therefore:
Triangle DEF is similar to Triangle DGH.
Class work
• Check solutions to Lesson 18.
• Copy down notes and examples
• Do Lesson 18(2) worksheet.