Geom Ch. 7.2.notes
January 31, 2017
Solve the proportion.
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6. Warm Up
Jan 28­9:32 PM
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Geom Ch. 7.2.notes
January 31, 2017
Jan 28­9:33 PM
How are similar polygons related?
Essential Question
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Geom Ch. 7.2.notes
January 31, 2017
Core Concept
In the diagram, RST XYZ.
a. Find the scale factor from RST to XYZ.
b. List all pairs of congruent angles.
c. Write the ratios of the corresponding side
lengths in a statement of proportionality.
Example 1
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Geom Ch. 7.2.notes
January 31, 2017
1. In the diagram, JKL PQR. Find the scale factor from JKL to PQR. Then list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality.
Monitoring Progress 1
In the diagram, DEF MNP.
Find the value of x.
Example 2
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Geom Ch. 7.2.notes
January 31, 2017
In the diagram, TPR XPZ.
Find the length of the altitude .
Example 3
2. Find the value of x. 3. Find KM.
Monitoring Progress 2­3
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Geom Ch. 7.2.notes
January 31, 2017
PERIMETERS OF SIMILAR POLYGONS
Theorem
A town plans to build a new swimming pool. An Olympic pool is rectangular with a length of 50 meters and a width of 25 meters. The new pool will be similar in shape to an Olympic pool but will have a length of 40 meters. Find the perimeters of an Olympic pool and the new pool.
Example 4 6
Geom Ch. 7.2.notes
January 31, 2017
4. The two gazebos shown are similar pentagons. Find the perimeter of Gazebo A.
Monitoring Progress 4
AREAS OF SIMILAR POLYGONS
Theorem
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Geom Ch. 7.2.notes
January 31, 2017
In the diagram, ABC DEF. Find the area of DEF.
Example 5
5. In the diagram, GHJK LMNP. Find the area of LMNP.
Area of GHJK = 84 m2
Monitoring Progress 5
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Geom Ch. 7.2.notes
January 31, 2017
Decide whether ABCDE and KLQRP are similar. Explain your reasoning.
Example 6
Refer to the floor tile designs below. In each design, the red shape is a regular hexagon.
Tile Design 1 Tile Design 2
6. Decide whether the hexagons in Tile Design 1 are similar. Explain.
7. Decide whether the hexagons in Tile Design 2 are similar. Explain.
Monitoring Progress 6­7
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