Assignment P. 384-387: 1-4, 7, 8, 10, 12, 14-17, 20, 30, 31, 32, 36, 41, 42 P. 391-395: 4, 6-8,...
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Transcript of Assignment P. 384-387: 1-4, 7, 8, 10, 12, 14-17, 20, 30, 31, 32, 36, 41, 42 P. 391-395: 4, 6-8,...
![Page 1: Assignment P. 384-387: 1-4, 7, 8, 10, 12, 14-17, 20, 30, 31, 32, 36, 41, 42 P. 391-395: 4, 6-8, 10-14, 33, 39, 40 Challenge Problems.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649e605503460f94b5bb7c/html5/thumbnails/1.jpg)
Warm-Up
Since they are polygons, what two things must be true about triangles if they are similar?
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Similar Polygons
Two polygons are similar polygons iff the corresponding angles are congruent and the corresponding sides are proportional.
MAIZCORN ~
ZMNC
IZRN
AIOR
MACO
ZNIR
AOMC
C
OR
N
C
OR
NM
A
I
Z
Similarity Statement:
Corresponding Angles:
Statement of Proportionality:
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Example 1
Triangles ABC and ADE are similar. Find the value of x.
6 cm
8 cm9 cm
xE
D
A
B
C
HINT: separate the diagram into 2 distinct triangles.
x=4
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Example 2
Are the triangles below similar?
3
5
4 6
8
1053
37
Do you really have to check all the sides and angles?
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6.4-6.5: Similarity Shortcuts
Objectives:
1. To find missing measures in similar polygons
2. To discover shortcuts for determining that two triangles are similar
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Angle-Angle Similarity
AA Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
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Example 3
Determine whether the triangles are similar. Write a similarity statement for each set of similar figures.
Answer in your notebook
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Thales
The Greek mathematician Thales was the first to measure the height of a pyramid by using geometry. He showed that the ratio of a pyramid to a staff was equal to the ratio of one shadow to another.
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Example 4
If the shadow of the pyramid is 576 feet, the shadow of the staff is 6 feet, and the height of the staff is 5 feet, find the height of the pyramid.
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Example 5
In your notebook:
1) Find the missing value of the pyramid
2) Explain why Thales’ method worked to find the height of the pyramid?
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Example 6
If a person 5 feet tall casts a 6-foot shadow at the same time that a lamppost casts an 18-foot shadow, what is the height of the lamppost?
15’
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Example 7
Your eye is 168 centimeters from the ground and you are 114 centimeters from the mirror. The mirror is 570 centimeters from the flagpole. How tall is the flagpole?
840
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Side-Side-Side Similarity
SSS Similarity Theorem:
If the corresponding side lengths of two triangles are proportional, then the two triangles are similar.
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Side-Angle-Side Similarity
SAS Similarity Theorem:
If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the two triangles are similar.
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Example 8
Are the triangle pairs below similar? Why or why not?
Yes, corresponding sides are in the same proportion.
Yes, 2 corresponding sides are in proportion and the included angles are congruent.
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Example 9
Use your new conjectures to find the missing measure.
18
24
x
24
28
y
x=32y=21
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Example 10
Find the value of x that makes ΔABC ~ ΔDEF.
x=7