Download 7.2_SimilarPolygons

Warm-Ups
• The number of students that participate in
sports programs at Central High School is 520.
The total number of students in the school is
1850. Find the athlete-to-student ratio to the
nearest tenth.
• In ∆EFG, the ratio of the measures of the
angles is 5:12:13, and the perimeter is 90
centimeters. Find the measures of the angles.
Happy Thursday!
Today:
Warm-Ups
Similar Polygons Activity
Similar Polygons Notes
• CC.9-12.G.SRT.5- Use congruence and
similarity criteria for triangles so solve
problems and prove relationships in geometric
figures.
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Use similarity statements.
Find and use the scale factor.
Use similar polygons.
Find perimeters of similar figures.
Activity
• Get into groups that are no larger than four.
• Cut out your triangles.
• Sort your triangles into groups based on
similar characteristics.
• Stop here! We are going to share!
Activity
• What are similar triangles?
• Group together similar triangles.
• Label your triangles 1a, 1b, 1c, 2a, 2b, 2c and 3a,
3b, 3c. Group 1 should be acute triangles, group 2
should be right triangles and group 3 should be
obtuse triangles. Letter a should go with your
smallest triangle, b the middle triangle and, and c
the largest triangle.
• Match up each groups corresponding angles.
Mark the angles.
Use Similarity Statements
• What did we say that similar polygons were?
What criteria do they meet?
• Two Polygons are similar if corresponding
angles are congruent and corresponding side
lengths are proportional.
Example:
Check!
Finding the Scale Factor
• If two polygons are similar then the ratio of
the lengths of two corresponding sides is
called the scale factor.
• What was our scale factor in example 1?
Example
• Step 1: Identify pairs of congruent angles
• Step 2: Show that the corresponding side
lengths are proportional
Using Similar Polygons
• In the diagram, △ DEF ~ △MNP. Find the value
of x.
Solution
Perimeters of Similar Polygons
• If two polygons are similar then the ratio of
their perimeters is equal to the ratios of their
corresponding side lengths.