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Transcript
CONGRUENCE VERSUS SIMILARITY
• QUESTIONS:
• If you look you are standing directly in front of a mirror looking at your
image what differences do you see if any?
• Is it the same as what’s actually there?
• Does the size or shape change?
• What about a 4 x 6 photo of yourself?
• Is it the same as what’s actually there?
• Does the size or shape change?
• The differences between your responses can easily be explained with
similarity and congruence.
CONGRUENCE AND
SIMILARITY
CONGRUENCE
https://learnzillion.com/lesson_plans/6426-identify-congruent-figures
• Congruence is defined as exactly equal in size and shape.
and angles are equal.
• Let’s look at an example.
This means all sides
Let’s determine if triangle ABC is congruent to
triangle A’B’C’. To do this we need to determine
if the points, sides, and angles are exactly same.
AB = 4
BC = 5
AC = 3
A = 90o
B = 35o
C = 55o
A’B’ = 4
B’C’ = 5
A’C’ = 3
A’ = 90o
B’ = 35o
C’ = 55o
What transformation took place?
CONGRUENCE
•
Let’s look at other examples.
Are the following two figures congruent?
Show proof of your determination.
CONGRUENCE
SIMILARITY
• Similarity is defined as having the
same shape, having proportional
corresponding sides, and
corresponding angles that are
equal
• When two polygons are similar, we
can write a similarity statement
using the symbol “~”
SIMILARITY
• Similarity can be determined
by finding the scale factor used
to make the dilation.
• If the same scale factor is used
for each side, it is the EXACT
same shape, AND all
corresponding angles are
congruent, then the figures are
similar.
• Let’s try other examples.