Lesson 11.1 ADV:
1. Homework Discussion
2. Similar Polygons
3. Dilations
Warm Up:
• Solve the proportion:
10
10+𝑧
=
35
56
Difference between Congruent and
Similar:
• Congruent: figures that have the same size
and shape.
• Similar: figures that have the same shape, but
not necessarily the same size.
Polygon/Circle Similarity:
• Are all equilateral triangles similar?
• Are all squares similar?
• Are all rectangles similar?
• Are all circles similar?
• How would you identify congruent circles?
Characteristics of Similar Polygons:
• Investigation #1: Use patty paper to complete
investigation #1
• Summary of Similar Polygons:
• Similar Polygons must have:
1)
2)
Example #1: Are the Polygons Similar? Explain.
a)
b)
Example #1: Are the Polygons Similar?
c)
Similarity Statement:
• If we are given that these 2 polygons are similar, we know
that:
• Corresponding angles
are congruent:
• Corresponding segments
are proportional:
Therefore, the similarity statement is:
Example #2:
• Determine the values of x and y given that the triangles are
similar.
Investigation #2:
• Dilation is an enlargement or a reduction of a figure that
maintains shape.
• This is a NON-RIGID transformation.
• The scale factor describes how we enlarge or reduce the
figure. Multiply each coordinate by the scale factor to get the
image. The scale factor is represented by the letter k.
Dilation Similarity Conjecture: If one polygon is a dilated
image of another polygon, then
_____________________________________.
Example #3:
• On your own graph paper, determine the coordinates of the
image after using the scale factor to create the dilation.
Homework:
• P. 585-587: 4, 8-10, 12-14, 16, 18, 22