Download Section 6.3

Chapter 6- Geometry
Section 6.3- Similar Triangles
Definition: Similar figures- figures that have the same shape and may be a
different size. The symbol ~ means “is similar to”.
Page 274- look at the triangles below. Using a protractor measure all of the
angles in each triangle. Fill in the chart with this information:
Triangle
Angle 1
Angle 2
Angle 3
∆ABC
A =
B =
C =
∆DEF
D =
E =
F =
∆GHI
G =
H =
I =
∆JKL
J =
K =
L =
∆MNO
M =
N =
O =
∆PQR
P =
Q =
R =
∆STU
S =
T =
U =
∆VWX
V =
W =
X =
Looking at this table, can you find pairs of angles that are related? What
is the relationship?
If two angles in a triangle are equal to corresponding angles in another
triangle, how is the third pair of corresponding angles related?
Now measure all the sides in each triangle. Fill in the chart:
Triangle
Side 1
Side 2
Side 3
∆ABC
AB =
BC =
AC =
∆DEF
DE =
EF =
DF =
∆GHI
GH =
HI =
GI =
∆JKL
JK =
KL =
JL =
∆MNO
MN =
NO =
MO =
∆PQR
PQ =
QR =
PR =
∆STU
ST =
TU =
SU =
∆VWX
VW =
WX =
VX =
Look for patterns in your measurements. Is there any relationships?
Which triangles are similar? _________________________________
How are the angles in these triangles related?_____________________
How are the sides related?___________________________________
What are the minimum sufficient conditions for similar triangles?
Look at the triangles below: which pairs are similar?
We can put the information from the triangles in a chart:
Triangles
Corresponding
Corresponding
angles
sides
∆ABC and ∆DEF
A=D
B=E
C=F
∆JKL and ∆PQR
∆STU and ∆VWX
Ratio of side
lengths
T=W
JK=3cm
KL=3cm
JL=4cm
PQ=9cm
QR=9cm
PR=12cm
1:3
1:3
1:3
ST=3cm
TU=2cm
VW=6cm
WX=4cm
1:2
1:2
Two triangles are similar if either of these conditions have been met:
1. In each pair of triangles the corresponding angles are equal (** two
matching angles are enough to conclude that triangles are similar
because I can find the measure of the third angle in each triangle!!)
2. In each pair of triangles the ratios of lengths of corresponding sides
are equal. In other words the lengths of corresponding sides are
proportional.
You can figure out if a triangle is similar using the following information:
1. AAA- In each pair of triangles the corresponding angles are equal.
2. SSS- In each pair of triangles the ratios of lengths of corresponding
sides are equal. In other words the lengths of corresponding sides
are proportional.
3. SAS- In each pair of triangles, one pair of matching angles and the
sides containing the angle in proportion.
Page 278 –solving problems involving similar triangles:
As part of the provincial Envirothon, Hannah’s team has to measure the
height of a particular tree. This tree casts a shadow 4.5m long. Hannah
places a stick upright at the end of the shadow. The stick is 60cm tall and
its shadow is 50cm long.
How tall is the tree? *** use similar triangles!!***
A
tree
height
D
60cm
or 0.6m
B
4.5m
C 50cm E
Or 0.5m
Remember all units must be the same!!
We can use the relationship between side lengths of similar triangles to
determine the height of the tree:
AB BC

DC CE
Fill in the side lengths:
AB
4.5m

Solve for AB by multiplying both sides by 0.6m
0.6m 0.5m
AB
4.5m
(0.6m)

(0.6m)
0.6m 0.5m
AB  5.4m the tree is 5.4 m tall.
Homework!! Page 279 # 1a, 2a, 3, 4, 7, 8, 9, 13a, 16