Download 8 - Garnet Valley School District

Geometry A Unit 8 Day 2 Notes
Warm-Up
Determine if the proportions are true.
1.
3 12

5 20
Proving Triangles Similar
2.
11 20

21 30
4. Determine if the two triangles are
congruent. If so, circle the reason.
A
AB is a median
3.
3 12 13.5


4 16 18
5. Determine if the triangles are congruent.
P
If so, complete the
congruence statement.
Y
H
T
YES
B
YES or NO
or
NO
A
SSS
SAS
AAS
ASA
 ___ ___ ___   ___ ___ ___
HL
I. Among the 7 triangles below, there are three pairs of similar triangles.
a. Put a box around one pair.
b. Circle a second pair
c. Cross out the remaining triangle that is not similar to any of the others.
R
N
Z
K
O
D
Q
S
L
M
H
E
G
F
V
C
A
P
U
T
B
II. That informal ability is nice, but formally, to know that we can use proportionality in
a certain diagram, we have to KNOW two figures are similar.
A.
_____________________________ similarity
What it means: If two angles of one triangle are congruent to two angles
of another triangle, then the triangles are similar.
Demonstration: To draw a triangle that is a scale drawing of  ABC, all we need to do is
to include two of its angles. The third angle will match, and the sides
will be scaled up or down automatically.
Choose one of the points “F” on the segment below.
B
A
Extend the rays that start at D and at your chosen F.
When the rays you are drawing cross, label the point
E.
C
Fill in the values of each side in
the proportion by measuring in
millimeters.
DE EF

AB BC

F
D

F
DF:AB = 1:2

F
DF:AB = 2:1

F
DF:AB = 3:1

F
DF:AB = 4:1

F
DF:AB = 5:1
DF:AB = 1:1
Do the sides you measured fit the same ratio as the one that compares DF and AB?

F
DF:AB = 6:1
B.
_____________________________ similarity
What it means: If the lengths of the corresponding sides of two triangles
are proportional, then the triangles are similar.
Ex. 2: Determine which pair of triangles is similar. Show any proportions used
and complete the similarity statement.

Place the numbers 16, 12, 12, 9, 8, 6 into the proportion

8
6
so that the proportion is true.
G
D
8
6
H
J
E
F
Similarity Statement:  ___ ___ ___ ~  ___ ___ ___
C.
_____________________________ similarity
What it means: If an angle of one triangle is congruent to an angle of a
second triangle and the lengths of the sides including these angles are
proportional, then the triangles are similar.
Demonstration: E and C are labeled at equal intervals, and so are B and D. Connect any E
to any B. Then connect C (with the same number as E) to D (with the same number as B).
B5
B4
B3
E4
E3
B2
E2
B1
E1
A
D1
D2
D3
D4
C1
C2
C3
C4
C5
Ex 3: Determine which pair of triangles is similar. Show any proportions used
and then list the pairs of congruent angles.
2
8
4
10
9
3
1
2
18
9
7
4
12
3
6
5
III. Summary and Examples
To determine if two triangles are similar, find matching angles and test sides in
proportions. The list of tests is SSS, SAS, and AA.
Determine whether the triangles are similar or not by testing for one of the following
types of symmetry. Show any proportions used.
M
Ex. 4:
Ex. 5: N
Z
4.5 4
B
B
24
46
V
YES or NO
L
46
X
C
Reason SSS SAS
 ___ ___ ___ ~  ___ ___ ___
AA
27
K
YES or NO Reason SSS SAS
 ___ ___ ___ ~  ___ ___ ___
AA
Ex. 6:
10
Ex. 7:
D
A
8
A
16
8
12
S
2.5
G
H
H
6
S
2
G
14
12
3
F
10
F
YES or NO
Reason SSS SAS AA
 ___ ___ ___ ~  ___ ___ ___
HW: Handout
YES or NO
Reason SSS SAS AA
 ___ ___ ___ ~  ___ ___ ___
D