Download Are the polygons congruent?

Are the polygons
congruent?
Section 7.1.1
Objective

G-CO.A
G-CO.B
Pumas will
 determine missing side lengths of similar polygons
 identify congruent polygons using the Pythagorean
Theorem
 identify congruent polygons using the Triangle
Angle Sum Theorem
 determine if two triangles are congruent by
comparing all three corresponding angle
measurements and all three corresponding side
lengths
Similar Polygons
Methods and Meanings

In your notebook, copy the following:
 Two polygons are similar if a sequence of rigid
transformations, followed possibly by a dilation
(enlargement or reduction), maps one polygon
onto the other.
 Two similar polygons have parts that correspond
(match up) with each other. For example, if ∆ABC
is similar to ∆DEF, then vertex A corresponds to
vertex D, C to F, and B to E. Also, AB corresponds
to DE, AC corresponds to DF, and BC corresponds to
EF.
Similar Polygons
Methods and Meanings
 In
your notebook, copy the following:
 Corresponding
angles of two similar polygons
have the same measures, but corresponding
side lengths might be different.
 The scale factor is the ratio that indicates how
the side lengths of two similar polygons are
related. The scale factor can be found by
writing a ratio between the lengths of any pair
of corresponding sides as
Similar Polygons
Methods and Meanings

In your notebook, copy the following:
 For example, the two similar triangles above are
related by a scale factor of because the side
lengths of the new triangle can be found by
multiplying any side length of the original triangle
by .
 A scale factor greater than 1 enlarges a shape
(makes it larger). A scale factor between zero and
1 reduces a shape (makes it smaller). If a scale
factor between two shapes is equal to 1, then the
two similar shapes are also congruent.
Congruent Polygons
Problem 7-3
Figures are drawn to scale
Congruent Polygons
Problem 7-3

In your notebook, answer the following:
Which of the polygons on the previous slide appear to be
congruent?
 What sequence of rigid transformations demonstrates the
congruence between the polygons?

 For
each pair of congruent polygons, what can you
say about the corresponding angle measures and side
lengths?
 Considering the definition of congruent polygons,
why would this have to be true?
Congruent Polygons
Problem 7-4
 In
your notebook, complete the following:
 Sketch
the triangles above on your paper.
 Are the triangles congruent?
 If so, what is the sequence of rigid
transformations that maps the triangle on the
left onto the triangle on the right?
 If the triangles are not congruent, explain why
not.
Congruent Polygons
Problem 7-5

Read the following and identify any questions you have
about them.
To represent the fact that two polygons are congruent,
use the symbol “ ”. For example, if there is a sequence
of rigid transformations that maps ΔABC onto ΔDEF, then
you know they are congruent and this can be stated as
ΔABC ΔDEF.
 The order of the letters in the name of each triangle
identifies which sides and angles correspond. For
example, the congruence statement ΔABC ΔDEF,
indicates that A corresponds to D and that BC
corresponds to EF.

Congruent Polygons
Problem 7-5
 In
your notebook, complete the following:
 Luis
wanted to write a statement to convey
that the two triangles above are congruent.
He started with “ΔMNP …”, but got stuck
because the triangles were not oriented the
same way.
 Complete Luis’s statement for him and
explain how you determined your answer.
Congruent Polygons
Problem 7-5
 In
your notebook, complete the following:
 What
sequence of rigid transformations
would map the triangle on the left onto the
one on the right?
 Label the triangles and then write a
congruence statement for the triangles
below which you sketched in your notebook.
Be prepared to justify your thinking.