Similar Triangles Postulates
Name_____________________
Hour___________
In the last lesson we learned the AA (Angle-Angle) postulate. Today we are going
to extend our “similarity tool box” to include other postulates.
Directions:
- In the box labeled “A” use a ruler to draw only two sides of a triangle with their
measurements between 2 cm and 5 cm. Label these measurements.
- In the box labeled “B” use a ruler to draw only two sides of a triangle with measurements
proportional to those drawn in box “A.” (Hint: increase the measurements by the same
amount.) Label these measurements.
- Next, connect your 3rd side to create the triangles. Measure these lengths and label them.
Are your 3rd sides of the triangles proportional to each other?
A
B
Follow up Questions:
When you know 2 sides of a triangle are proportional (you drew your example this way), will
your 3rd side always be proportional also?
Turn to a neighbor and compare. Use an additional paper to experiment if needed.
Are your two triangles in box “A” and “B” similar? (Borrow a protractor to measure the angles)
Similarity Practice 3
Name_________________________________________________________ Hour____________
Ready
1. How does the SSS postulate for similar triangles differ from the SSS postulate for congruent
triangles?
2. How does the SAS postulate for similar triangles differ from the SAS postulate for congruent
triangles.
Set
List the similar triangles in the following figures. Write the postulate or theorems that prove your
answer.
3.
4.
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B
110º
X
A
A
B
6 ft
70º
Y
4 ft
P
8 ft
12 ft
C
C
D
Use the diagram to complete Exercises 5-8.
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Q
L
P
𝑃𝐿
5.
𝑃𝑀
=
𝑃𝑄
6.
?
R
M
?
𝐿𝑄
𝑃𝑀
= 𝑀𝑅
7.
𝑃𝐿+𝐿𝑄
𝐿𝑄
=
?
𝑀𝑅
8. If 𝐿𝑄 = 9𝑐𝑚, 𝑃𝑀 = 8𝑐𝑚, 𝑎𝑛𝑑 𝑀𝑅 = 12𝑐𝑚, 𝑡ℎ𝑒𝑛 𝑃𝐿 = ___________cm.
Go!
Determine whether each pair of triangles is similar. Justify your answer.
9.
10.
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B
A
D
8
E
A
10
4
F
P
C
B
5
D
11.
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E
21
D
B
25
9
F
25/3
7
A 3
C
C