What are we going to do? CFU On your whiteboards, draw a right
triangle. Label the hypotenuse. Label the legs. Students, you
already know the parts of a right triangle. You also know how to
square and square root numbers. Now, we will find unknown lengths
of the hypotenuse and legs of right triangles using the Pythagorean
Theorem. Make Connection Learning Objective Activate Prior
Knowledge We will use the Pythagorean Theorem to find an unknown
length of a side. A right triangle is a triangle with a 90 angle.
The hypotenuse is the side opposite the right angle. The legs are
the two shorter sides of the right triangle. Right Triangle 2. 4.
40020 36119 32418 28917 25616 22515 19614 16913 Use the chart to
evaluate the following. 1. 3. Wednesday, 11/13/13 CA Standard:
7.MG3.3 Common Core State Standards 8.G.7
Slide 2
6 cm 8 cm The Pythagorean Theorem 1 describes the relationship
between the lengths of the sides of a right triangle. The
Pythagorean Theorem can be used to solve for an unknown side length
in a right triangle. For which triangle(s) could you use the
Pythagorean Theorem to find the unknown side length? How do you
know? Why can you not use the Pythagorean Theorem on the other
triangle(s)? In your own words, describe the Pythagorean theorem.
The Pythagorean Theorem describes _____. CFU Concept Development 1
statement which can be proven mathematically Vocabulary Pythagorean
Theorem If the triangle is a right triangle, then the square of the
first leg plus the square of the second leg is equal to the square
of the hypotenuse. 10 cm 6 cm 8 cm ? ft 5 ft 12 ft NOT a right
triangle The Pythagorean Theorem CANNOT be used: 9 11 ? 712 ? 9 9
?
Slide 3
Concept Development (Clarification and CFU) The Pythagorean
Theorem describes the relationship between the lengths of the sides
of a right triangle. If the triangle is a right triangle, then the
square of the first leg plus the square of the second leg is equal
to the square of the hypotenuse. Using the diagram below, describe
the relationship between the square of the legs and the square of
the hypotenuse of the right triangle. CFU 4 5 3 = hyp 2 leg 2
+
Slide 4
Determine 2 if the Pythagorean Theorem can be used. Identify 3
the hypotenuse and two legs of the right triangle. (record) Find
the unknown length of the side using the Pythagorean Theorem.
Substitute 4 the two known values and solve. Interpret 5 the
solution. Use the Pythagorean Theorem to find an unknown length of
a side. 1 2 3 4 a Skill Development/Guided Practice How did I/you
determine if the Pythagorean Theorem can be used? How did I/you
identify the hypotenuse and two legs of the right triangle? How did
I/you find the unknown side length using the Pythagorean Theorem?
CFU 1 2 3 Pythagorean Theorem leg 2 + leg 2 = hyp 2 The Pythagorean
Theorem describes the relationship between the lengths of the sides
of a right triangle. 1. Find the length of. ( means the line
segment starting at point Y and ending at point Z.) 2. Find the
length of. 5 in 12 in 9 cm 12 cm leg = hyp = The length of the
___________ is _______. leg = hyp = The length of the ___________
is _______. 2 figure out 3 find (synonym) 4 replace (synonym) 5
explain Vocabulary
Slide 5
Skill Development/Guided Practice (continued) Determine if the
Pythagorean Theorem can be used. Identify the hypotenuse and two
legs of the right triangle. (record) Find the unknown length of the
side using the Pythagorean Theorem. Substitute the two known values
and solve. Interpret the solution. Use the Pythagorean Theorem to
find an unknown length of a side. 1 2 3 4 a How did I/you determine
if the Pythagorean Theorem can be used? How did I/you identify the
hypotenuse and two legs of the right triangle? How did I/you find
the unknown side length using the Pythagorean Theorem? CFU 2 2 3
Pythagorean Theorem leg 2 + leg 2 = hyp 2 The Pythagorean Theorem
describes the relationship between the lengths of the sides of a
right triangle. 3. Find the length of side p.4. Find the length of
side w. 6 in 10 in p 4 cm 5 cm w leg = hyp = The length of the
___________ p is _______. leg = hyp = The length of the ___________
w is _______.
Slide 6
Determine if the Pythagorean Theorem can be used. Identify the
hypotenuse and two legs of the right triangle. (record) Find the
unknown length of the side using the Pythagorean Theorem.
Substitute the two known values and solve. Interpret the solution.
Use the Pythagorean Theorem to find an unknown length of a side. 1
2 3 4 a How did I/you determine if the Pythagorean Theorem can be
used? How did I/you identify the hypotenuse and two legs of the
right triangle? How did I/you find the unknown side length using
the Pythagorean Theorem? CFU 1 2 3 Pythagorean Theorem leg 2 + leg
2 = hyp 2 The Pythagorean Theorem describes the relationship
between the lengths of the sides of a right triangle. 5. In the
figure below, D is the midpoint of, and is perpendicular to. What
is the length of ? 6. In the figure below, H is the midpoint of,
and is perpendicular to. What is the length of ? A D C B 20 in 26
in H E F G 24 in 20 in leg = hyp = The length of the ___________ is
_______. leg = hyp = The length of the ___________ is _______.
Skill Development/Guided Practice (continued)
Slide 7
Determine if the Pythagorean Theorem can be used. Identify the
hypotenuse and two legs of the right triangle. (record) Find the
unknown length of the side using the Pythagorean Theorem.
Substitute the two known values and solve. Interpret the solution.
Use the Pythagorean Theorem to find an unknown length of a side. 1
2 3 4 a How did I/you determine if the Pythagorean Theorem can be
used? How did I/you identify the hypotenuse and two legs of the
right triangle? How did I/you find the unknown side length using
the Pythagorean Theorem? CFU 1 2 3 Pythagorean Theorem leg 2 + leg
2 = hyp 2 The Pythagorean Theorem describes the relationship
between the lengths of the sides of a right triangle. 7. In the
figure below, M is the midpoint of, and is perpendicular to. is 15
cm. is 16 cm. What is the length of ? 8. In the figure below, Q is
the midpoint of, and is perpendicular to. is 24 cm. is 14 cm. What
is the length of ? L M J K O Q P N leg = hyp = The length of the
___________ is _______. leg = hyp = The length of the ___________
is _______. Skill Development/Guided Practice (continued)
Slide 8
Using the Pythagorean Theorem will help you find the distance
between locations. Using the Pythagorean Theorem will help you do
well on tests. 1 Does anyone else have another reason why it is
relevant to use the Pythagorean Theorem? (PairShare) Why is it
relevant to use the Pythagorean Theorem? You may give me one of my
reasons or one of your own. Which reason is more relevant to you?
Why? CFU 2 Relevance The Pythagorean Theorem describes the
relationship between the lengths of the sides of a right triangle.
How long is the Salinas River from King City to Soledad? Salinas
River King City Soledad 16mi 12mi Sample Test Question:
Slide 9
Summary Closure Access Common Core The Pythagorean Theorem
describes the relationship between the lengths of the sides of a
right triangle. Determine if the Pythagorean Theorem can be used.
Identify the hypotenuse and two legs of the right triangle.
(record) Find the unknown length of the side using the Pythagorean
Theorem. Substitute the two known values and solve. Interpret the
solution. Use the Pythagorean Theorem to find an unknown length of
a side. 1 2 3 4 a With which triangle on the left could you use the
Pythagorean Theorem to find the unknown length? Explain why you
cannot use the Pythagorean Theorem on the other. 10 12 ? A 6 6 ? B
Pythagorean Theorem leg 2 + leg 2 = hyp 2 Skill Closure 1. Find the
length of side d. 8 cm 6 cm d leg = hyp = The length of the
___________ d is _______. What did you learn today about using the
Pythagorean Theorem? (Pair-Share) Use words from the word bank.
Word Bank Pythagorean Theorem right triangle side hypotenuse leg
length
Slide 10
Independent Practice Determine if the Pythagorean Theorem can
be used. Identify the hypotenuse and two legs of the right
triangle. (record) Find the unknown length of the side using the
Pythagorean Theorem. Substitute the two known values and solve.
Interpret the solution. Use the Pythagorean Theorem to find an
unknown length of a side. 1 2 3 4 a Pythagorean Theorem leg 2 + leg
2 = hyp 2 The Pythagorean Theorem describes the relationship
between the lengths of the sides of a right triangle. 1. Find the
length of. S T R 15 ft 8 ft 2. Find the length of side g. 20 in 25
in g leg = hyp = The length of the ___________ is _______. leg =
hyp = The length of the ___________ g is _______.
Slide 11
Determine if the Pythagorean Theorem can be used. Identify the
hypotenuse and two legs of the right triangle. (record) Find the
unknown length of the side using the Pythagorean Theorem.
Substitute the two known values and solve. Interpret the solution.
Use the Pythagorean Theorem to find an unknown length of a side. 1
2 3 4 a Pythagorean Theorem leg 2 + leg 2 = hyp 2 The Pythagorean
Theorem describes the relationship between the lengths of the sides
of a right triangle. Independent Practice (continued) 3. In the
figure below, W is the midpoint of, and is perpendicular to. What
is the length of ? 4. In the figure below, B is the midpoint of,
and is perpendicular to. is 4 cm. is 6 cm. What is the length of ?
24 in 15 in leg = hyp = The length of the ___________ is _______.
leg = hyp = The length of the ___________ is _______.
Slide 12
Periodic Review 1 1. Find the length of side c.2. Find the
length of side y. 24 m 10 m c 24 in 25 in y leg = hyp = The length
of the ___________ c is _______. leg = hyp = The length of the
___________ y is _______. 3. In the figure below, O is the midpoint
of, and is perpendicular to. is 20 cm. is 30 cm. What is the length
of ? leg = hyp = The length of the ___________ is _______.
Slide 13
Access Common Core For questions 1a1d, choose Yes or No to
indicate whether the statement is true or false. 12 m 5 m p 1a.
YesNo The Pythagorean Theorem can be used to solve for the unknown
side length because the triangle is a right triangle. 1b. YesNo The
unknown side length (p) can be solved for using the equation 5 2 +
p 2 = 12 2 1c. YesNo The length of the unknown side (p) will be
shorter than the other two sides. 1d. YesNo The length of side p is
13 m.
Slide 14
Access Common Core 80 5545 8 in 10 in q Greg used the
Pythagorean Theorem in the triangle. He found that the unknown side
length (q) was 6 in. Explain why Greg is incorrect using pictures,
math, or words. Periodic Review 2 1. In the figure below, Y is the
midpoint of, and is perpendicular to. is 16 cm. is 60 cm. What is
the length of ? 2. Find the length of. N M O 20 in 21 in leg = hyp
= The length of the ___________ is _______. leg = hyp = The length
of the ___________ is _______.
Slide 15
2. Find the length of side c. 3. In the figure below, E is the
midpoint of, and is perpendicular to. What is the length of ? E D G
F 18 in 15 in 24 m 18 m c leg = hyp = The length of the ___________
c is _______. leg = hyp = The length of the ___________ is _______.
1. Find the length of side a. 36 cm 39 cm a leg = hyp = The length
of the ___________ a is _______. Periodic Review 3
Slide 16
Access Common Core Lilias House Kurts House 9 miles b 15 miles
Kurt is driving to Lilias house. On a straight line, his house is
15 miles from Lilias, however, he must drive to her house using
roads. He heads west for 9 miles then turns right heading north.
How far north does Kurt have to travel before reaching Lilias
house? Explain your answer below using pictures, math, or
words.