Download Congruent Figures

CONGRUENT FIGURES
&
PYTHAGOREAN
THEOREM
Mrs. Samuelian
CAHSEE Prep
Congruent Figures
7MG 3.4 Students will identify congruent figures and match
corresponding sides and angles.
Vocabulary:
Angle- A figure formed by two rays with a common endpoint-the
common endpoint is called the vertex of the angle
Congruent Figures- Two or more figures that are the same shape and
size
Introduction
When two or more shapes are alike, they are called congruent
shapes.
Two or more shapes are congruent if they can be placed one on top
of each other and all the points match.
This means that all the matching sides have the same length and all
matching angles have the same measure.
Understanding the Symbols
Notice the tick mark on the top of each of the two triangles.
-------
-------
This mark means that the segments AC and DF are congruent.
The symbol ≅ is used to show two objects are congruent.
------- -------
Therefore, AC ≅ DF.
Look for clues to help you match up sides and angles.
Tick marks and angle marks are a great way to indicate side and angle
congruence.
Polygons with sides that have the same number of tick marks means
that the sides are congruent.
Angles with an equal number of tick marks indicate congruent angles.
Identifying Corresponding Parts of
Congruent Figures
• The sides and angles that match and have the same measure are
called corresponding parts. The two shapes below are congruent
triangles.
--------
-----
• Side AB corresponds to side XY, since they have the same length.
Pythagorean Theorem
7MG 3.3 Students will use the Pythagorean theorem to find the
length of the hypotenuse or to find the length of the missing leg of a
right triangle.
Vocabulary
Hypotenuse: The side opposite the right angle in a right triangle (the
longest side)
Pythagorean theorem: The sum of the squares of the lengths of the
legs in a right triangle is equal to the square of the length of the
hypotenuse
Right triangle: A triangle with one 90 degree angle
Square root: One of the two equal factors of a number
Introduction
If you know the lengths of both legs of a right triangle, you can find the
hypotenuse length using the Pythagorean theorem, a2 + b2 = c2
Also, if you know the hypotenuse length and the length of one of the
legs, then you can find the missing leg length!
Square Roots
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9
√100 = 10
√121 = 11
√144 = 12
√169 = 13
Since 12 = 1
Since 22 = 4
Since 32 = 9
Since 42 = 16
Since 52 = 25
Since 62 = 36
Since 72 = 49
Since 82 = 64
Since 92 = 81
Since 102 = 100
Since 112 = 121
Since 122 = 144
Since 132 = 169
3 cm
5 cm
?
• What information are you given?
• What information are you looking for?
• Write the Pythagorean theorem, filling in the information that you
know.
• Square each of the known values.
• Solve this equation algebraically to find the unknown side length.
3 cm
5 cm
a2 + b 2 = c2
a2 + 3 2 = 52
a2 + 9 = 25
a2 = 16
√a2 = √16
a=4
?