Download (AA) Similarity Postulate - Collingswood High School

8.4
Similar Triangles
We are now going to look specifically at the properties of similar triangles.
Ex 1. In the diagram, ABC ~ DEF.
C
34°
a. Write a statement of proportionality.
20
D
E
3
b. Find the measure of angle CDE.
c. What is the scale factor of ABC to DEF?
A
79°
B
12
d. Find DC and AD.
Angle-Angle (AA) Similarity Postulate
If two angles of one triangle are congruent to
two angles of another triangle, then
Determine whether SNM~JFL
2.
S 75° F
L
48°
N
3.
57°
L
60°
M
60°
M
57°
60°
J
60°
J
N
F
S
Ex. 4 In the diagram, JKL ~ MNP.
a. Find m  J, m  N, m  P.
4
J
N
K
3
53°
L
5
8
b. Find the scale factor of JKL to MNP.
M
c. Find MP and PN.
37°
P
8.5
Proving Triangles are Similar
Side-Side-Side (SSS) Similarity Theorem
If the lengths of the corresponding sides of two
triangles are proportional, then
Side-Angle-Side Similarity Theorem
If an angle of one triangle is congruent to an angle of
a second triangles and the lengths of the sides
including these angles are proportional, then
Draw and label lengths of 2 triangles that are similar to the one given.
1.
4
9
2.
8
6
3
3.
6.8
3.5
7
Given: SP = 4, PR = 12, SQ = 5, QT = 15
Prove: RST ~ PSQ
S
4
P
12
R
5
Q
15
T
8.6
Proportions and Similar Triangles
Q
T
Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects
the other two sides, then
S
U
Q
R
T
Converse of the Triangle Proportionality Theorem
If a line divides two sides of a triangle proportionality,
then
R
S
U
If three parallel lines intersect two
transversals, then
A
If a ray bisects an angle of a triangle, then
D
C
B
Similarity Activity
What you need:
-a cartoon picture
-ruler
-pencil
-graph paper
-colored pencils/crayons
-scissors
Directions:
1. Draw a 1 cm by 1 cm grid on your picture.
2. Use your grid as a guide to enlarge the picture. You may not be able to fit the
entire picture on the graph paper.
3. Color in your character.
4. When you are done your character, see Ms. Goulburn for a square piece from
another picture, and a piece of paper with a large square drawn on it.
5. Enlarge your small piece to the large square, and cut it out.
6. Write the location (A1, E3, etc.) on the back of your enlargement.
7. When everyone is done, we will put together everyone’s squares to see the big
picture.
Similarity Activity
What you need:
-a cartoon picture
-ruler
-pencil
-graph paper
-colored pencils/crayons
-scissors
Directions:
1. Draw a 1 cm by 1 cm grid on your picture.
2. Use your grid as a guide to enlarge the picture. You may not be able to fit the
entire picture on the graph paper.
3. Color in your character.
4. When you are done your character, see Ms. Goulburn for a square piece from
another picture, and a piece of paper with a large square drawn on it.
5. Enlarge your small piece to the large square, and cut it out.
6. Write the location (A1, E3, etc.) on the back of your enlargement.
7. When everyone is done, we will put together everyone’s squares to see the big
picture.