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DO NOW Wednesday, November 6, 2013
What are we going to do?
CFUWe will use the Pythagorean Theorem1 to calculate the sides of Right Triangles2.
Learning Objective
Activate Prior Knowledge
Tuesday, November 5, 2013 Name: ________________________ Per: __
1
Vocabulary
2 Special Triangles that contain one Right (90 degree) angle.
Vocabulary
Two Dimensional Shapes come in many sizes and numbers of sides.
Triangles have exactly three sides.
Triangles add up to 180 degrees.
Special triangles have unique characteristics, such as Right triangles.
What else do you know about triangles?
Concept Development
Right Triangles contain two legs and a hypotenuse.• The Hypotenuse1 is the side of the triangle across from the right angle
(ALSO: it is the longest side).• There are two legs2 which can be the same size or different sizes. They are
shorter than the hypotenuse
How many legs does a right triangle have?
CFU
2 Two shorter sides of a Right Triangle.
Vocabulary
1 The longest side of a Right Triangle across from the right angle.
Vocabulary
What part of the triangle is the hypotenuse across from?
CFU
Side Length PR or RP
FG is a Hypotenuse
PQ or QP and QR or RQ
GH is a leg
There are 2 legs.
The hypotenuse is across from the right angle.
Concept Development
In the triangles shown, what does the letter c represent?
CFU
162 122 162
144 256
400
20 -20
20 -20
20Can a Hypotenuse or Leg length ever be negative?
CFU
Concept Development
What is the formula for the Pythagorean Theorem?
CFU
82 152
64 225
289
289
17 -17
17 -17
17
Concept Development
49
625
13 in.HINT: Use the Pythagorean Theorem.
a2 + b2 = c2
52 + 122 = 132
25 + 144 = 169
Equation is balanced, therefore this is a right triangle.
Skill Development/Guided Practice
32 + 42 = c2
9 + 16 = c2
25 = c2 c = 5
62 + 82 = c2
36 + 64 = c2
100 = c2 c = 10
Skill Development/Guided Practice
a2 + b2 = c2
52 + 122 = c2
25 + 144 = c2
169 = c2
= c
13 = c
169
a2 + b2 = c2
62 + 82 = c2
36 + 64 = c2
100 = c2
= c
10 = c
100
c
c
What is the diagonal line across from the right angle called in a right triangle?
CFU
Relevance
Television are advertised by the length of their diagonal screen size. Example: A 27 inch TV has a diagonal (hypotenuse) measure of 27 inches.
Crazy Eddie’s Electronics in San Jose is having a Veteran’s Day Sale on all TV’s that are 40 inches and larger.
Is the TV to the left going to be on sale? Explain your reasoning.
How can you use the Pythagorean Theorem to explain the dimensions of the TV?
What is the length of the diagonal on the TV shown above?
242 + 322 = c2
576 + 1024 = c2
1600 = c2
= c 40 = c1600
YES, the TV will be on sale because it is at least 40 inches.
What did you learn today about the Pythagorean Theorem? (Pair-Share) Use words from the word bank.
Summary Closure
Word Bank
Skill Closure
Leg HypotenusePythagorean Right Triangle
How can we prove whether this triangle is a Right Triangle or Not?
a2 + b2 = c2
32 + 42 = c2
9 + 16 = c2
5 = c
If a2 + b2 = c2, then you have proven a right triangle.
Independent Practice
Independent Practice
USE THIS SPACE FOR ANY SCRATCH WORK. WHICH TERM IS A, WHICH IS B, WHICH IS C?
The triangle to the right is for a reference only. You need to draw your own, and label the lengths of the sides.