Pythagorean Theorem, Classifying triangles, Right Triangles

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Pythagorean Theorem, Classifying triangles,Right
Triangles

• By Matthew B.
• And
• Troy L.

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Right Triangles

• Works only for RIGHT triangles!!
• Hypotenuse- The longest side of a right triangle.
  It is also known as C
• Legs- The two shortest sides of a right triangle.
  Known as A and B. These are attached to the
  right angle.
• Hint- A Right triangle is a triangle with a 90
  degree angle.

Above, are the labeled Hypotenuse and legs.
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Hidden Tricks!

• You can use hashes to help you tell if angles are
  the same, or sides are the same. For example, a
  right triangle is signified with a square, where
  the 90 angle is located.

Other angles are signified with curves, for
example two similar angles will have the same
number of curves.
(The sum of the Interior angles of a triangle
must be 180.)
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Continued

• Also you can use hashes to tell if the lengths of
  sides are the same.

The sides with one hash have the same length, and
the side with two is a different length.
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Pythagorean Theorem
Example Finding Hypotenuse To find the length of
the hypotenuse, use the Pythagorean
theorem A² B² C² Begin with the
formula 50²40²C² Fill in known
values 25001600C² Simplify 4100C² Solve for
C SQRT of 4100C 64.03C (Round to nearest
Hundredth)

• In any right triangle, the sum of the squares of
  the lengths of the legs is equal to the square of
  the length of the hypotenuse.
• For example, the legs are represented by A, and
  B. The hypotenuse is represented by the letter
  C.
• A²B²C² is the formula. To find the lengths of
  the hypotenuse and legs, fill in lengths for each
  letter.

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Checking for Understanding

• What is the longest side of a right triangle
  called?
• What are the Legs?
• What is the Pythagorean Theorem?
• And what is the Formula?

Hypotenuse Shortest, attached to the right
angle Strategy to find missing lengths of a
right triangle A²B²C²
Click for Answers
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PRACTICE MAKES PERFECT!

• Can you form a right triangle with the following
  sets of numbers? Explain.
• 1) 7, 8, 9
• 2) 5, 6, 10

No, because 7²8² doesnt 10² No, because
5²6² doesn't 10²
Click for Answers, but try to solve before
looking at answer.
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How To.

• Solve for the Legs, of a right triangle
• To solve for the legs, you follow the same
  process.

To solve, first set up the equation. A²B²C² 15²
B²30² Place in the values that you
know 225B²900 Solve the
squares -225B²-225 Solve B²775
225 cancels out, and 900-225775 SQRT
of 775B Find Square root of 775 B 27.8
(Rounded to nearest tenth)
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Classifying Triangles By Side

• There are two ways that you can classify
  triangles. You can classify by sides, or by the
  angles.
• To classify Triangles by their sides, you have to
  look at the lengths of each side. There is an
  equilateral triangle, an Isosceles triangle, and
  there is the Scalene triangle. An equilateral
  triangle has 3 sides with the same length. An
  Isosceles Triangle Has two equal sides, and one
  different side. A scalene triangle is a triangle
  with three different side lengths.

Isosceles Equilateral Scalene
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Classifying Triangles By Angle
To classify Triangles by Angles, you must know
the measures of the angles. If the sum of the
angles measures do not come out to be 180, then
the triangle is messed up. The sum of the
Interior angles of a triangle must be 180. There
are three types of triangles, if you are to
measure by angle. (Acute, Right and Obtuse) An
acute triangle has three acute angles(lt90), a
right triangle has one right(90) angle and two
acute angles, and an obtuse triangle has one
obtuse angle(gt90) and two acute angles.
Right Triangle Acute Triangle
Obtuse Triangle
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Name the Triangle!
Answers on next slide
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ANSWERS
1) Isosceles Triangle 2) Equilateral Triangle 3) Scalene Triangle
4) Right Triangle 5) Acute Triangle 6) Obtuse Triangle
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Practice and Review

• What is the longest Side of a Right Triangle?
• What is the shortest?
• FIND THE MISSING LENGTHS

Hypotenuse
Legs
6 ft.²
64.03 ft.²
Click for Answers (One at a time)
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Doing Good!

• Solve for the missing Side
• Click for answers

7.9 Inches
13 Centimeters
3.5 feet
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KEEP IT UP!

• Classify the following triangles by side and then
  by angle.

Scalene, Right Triangle
Isosceles, Acute Triangle
Click for answers, one at a time)
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Congrats!

• You now know the basics of the Pythagorean
  theorem, and classifying triangles! I hope you
  learned a lot!

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Created by

• Troy L.
• Matthew Brown