Transcript Pythagorean Theorem, Classifying triangles

Pythagorean Theorem, Classifying triangles,
Right Triangles
By: Matthew B.
And
Troy L.
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.
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°.)
…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.
Pythagorean Theorem
• 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”.
• A²+B²=C² is the formula. To
find the lengths of the
hypotenuse and legs, fill in
lengths for each letter.
Example: Finding
Hypotenuse
To find the length of the hypotenuse,
use the Pythagorean theorem
A² +B² =C² Begin with the formula
50²+40²=C²
Fill in known values
2500+1600=C² Simplify
4100=C² Solve for “C”
SQRT of 4100=C
64.03=C (Round to nearest Hundredth)
Checking for Understanding
• What is the longest side of a right triangle called?
Hypotenuse
• What are the Legs?
Shortest, attached to the right angle
• What is the Pythagorean Theorem?
Strategy to find missing lengths of a right triangle
• And what is the Formula?
A²+B²=C²
Click for Answers
PRACTICE MAKES PERFECT!
• Can you form a right triangle with the
following sets of numbers? Explain.
• 1) 7, 8, 9
No, because 7²+8² doesn’t = 10²
• 2) 5, 6, 10
No, because 5²+6² doesn't = 10²
Click for Answers, but try to solve before looking at answer.
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.
A²+B²=C²
15²+B²=30²
Place in the values that you know
225+B²=900
Solve the squares
-225+B²=-225
Solve
B²=775
225 cancels out, and 900-225=775
SQRT of 775=B
Find Square root of 775
B= 27.8
(Rounded to nearest tenth)
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
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(<90°), a
right triangle has one right(=90°) angle and two acute angles, and an obtuse
triangle has one obtuse angle(>90°) and two acute angles.
Right Triangle
Acute Triangle
Obtuse Triangle
Name the Triangle!
Answers on next slide
ANSWERS
1) Isosceles
Triangle
2) Equilateral
Triangle
3) Scalene
Triangle
4) Right
Triangle
5) Acute
Triangle
6) Obtuse
Triangle
Practice and Review
• What is the longest Side of a Right Triangle?
Hypotenuse
• What is the shortest?
Legs
• FIND THE MISSING LENGTHS:
6 ft.²
64.03 ft.²
Click for Answers (One at a time)
Doing Good!
•
Solve for the missing Side
7.9 Inches
13 Centimeters
3.5 feet
•
Click for answers
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)
Congrats!
• You now know the basics of
the Pythagorean theorem, and
classifying triangles! I hope
you learned a lot!
Created by:
Troy L. &
Matthew Brown