1. Learning Objective
What are we going to do?
What does apply & segment mean?
Apply & segment means ___________.
CFU
We will apply1 the Distance and the Midpoint formulas to determine the Segment2 Length.
Activate Prior Knowledge
To find the length of a line segment, use the Pythagorean theorem to calculate the length of the hypotenuse.
On your whiteboard,
write the Pythagorean Theorem:
Students, you already know the Pythagorean theorem. Now, we will apply the Distance and the Midpoint formulas to determine the Segment Length.
Make Connection
Find the length of the hypotenuse.
1 put to use
2 part of a line cut into small parts or sections.
Vocabulary

2. Concept Development
The most basic figures in geometry are undefined1 terms, which cannot be defined using other figures.
On your whiteboard, Identify the following: . E.
In your own words, describe the undefined terms.
In geometry, undefined terms are _____.
CFU
Point
Endpoint
Line
Ray
plane
1 "three undefined terms of geometry"
Vocabulary

3. Concept Development
Collinear means that points are on the same line, coplanar means “together on the same plane.”
Note: co- usually means together or joint. For example, coauthors author a book together.
Use the Distance Formula to determine the length of each segment in the figure shown.

4. Concept Development
You can use the Midpoint Formula to find the midpoint of a segment on the coordinate plane.
On your whiteboard, determine the coordinates of the midpoint for each segment. Identify the quadrant that each midpoint lies in. 1. 2. II I

5. The length of the ___________
Skill Development/Guided Practice
The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle.
Determine2 if the Pythagorean Theorem can be used.
Identify3 the hypotenuse and two legs of the right triangle. (record)
Find the unknown length of the side using the Pythagorean Theorem.
Substitute4 the two known values and solve.
Interpret5 the solution.
Use the Pythagorean Theorem to find an unknown length of a side. 1 2 3 4 a
How did I/you know if the Pythagorean Theorem can be used?
How did I/you identify the hypotenuse/legs of the triangle?
How did I/you find the unknown side length?
CFU 1 2 3
1. Find the length of YZ.
The length of the ___________
YZ is _______.
2. Find the length of XZ.
XZ is _______.
leg2 + leg2 = hyp2
9 cm
12 cm
leg =
hyp =
12 cm
leg =
hyp =
12 in
9 cm
5 in
15 cm
5 in
12 in
? cm
? in
13 in
leg2 + leg2 = hyp2
leg2 + leg2 = hyp2
= hyp2
= hyp2
= hyp2
= hyp2 √
225 = hyp2 √ √
169 = hyp2 √
2 figure out
3 find (synonym)
4 replace (synonym)
5 explain
Vocabulary
15 = hyp
13 = hyp
hypotenuse
hypotenuse
15 cm
13 in

6. Solving Math Problems Solving Math Problems
Skill Development/Guided Practice (continued)
How did I/you determine what the question is asking?
How did I/you determine the math concept required?
How did I/you determine the relevant information?
How did I/you solve and interpret the problem?
How did I/you check the reasonableness of the answer?
CFU 2 1 3 4 5
Solving Math Problems
1 Determine what the question is asking.
2 Determine the math concept required.
3 Determine relevant information.
4 Solve the problem, then interpret the answer.
5 Check the reasonableness of your answer.
1. The sign shows distances from a rest stop to the exits for different towns along a straight section of highway. The state department of transportation is planning to build a new exit to Freestone at the midpoint of the exits for Roseville and Edgewood. When the new exit is built, what will be the distance from the exit for Midtown to the exit for Freestone?
2. On a town map, each unit of the coordinate plane represents 1 mile. Three branches of a bank are located at A(−3, 1), B(3, 4), and C(3, −2). A bank employee drives from Branch A to Branch B and then drives halfway to Branch C before getting stuck in traffic. What is the minimum total distance the employee may have driven before getting stuck in traffic? Round to the nearest tenth of a mile if necessary.
Solving Math Problems
1 What am I trying to find?
2 What do I know about this idea?
3 What amounts do I know?
4 Solve the problem or answer the question.
5 Did I answer all parts of the question?
Roseville to Edgewood exits is 59 − 35 = 24 mi, so the distance from the Roseville to Freestone exits will be ½ (24) = 12 mi. Midtown to Roseville exits is 35 − 17 = 18 mi, so the distance from the Midtown to Freestone exits will be = 30 mi.

7. How long is the Salinas River from King City to Soledad?
Relevance
The Pythagorean Theorem, Distance and the Midpoint formulas describes the relationship between the lengths of the sides of a right triangle. 1
Using the Pythagorean Theorem will help you find the distance between locations.
How long is the Salinas River from King City to Soledad?
Salinas River
Soledad
16mi
12mi
King City
leg
hyp 2
Using the Midpoint formula will help you do well on tests.
Does anyone else have another reason why it is relevant to use the Pythagorean Theorem, Distance and the Midpoint formulas? (Pair–Share) Why is it relevant to use the these formulas? You may give me one of my reasons or one of your own. Which reason is more relevant to you? Why?
CFU

8. The length of the ___________
The Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle.
Word Bank
Skill Closure
1. Find the length of side d.
The length of the ___________
p is _______.
leg2 + leg2 = hyp2
8 cm
6 cm d
= hyp2
leg =
hyp =
6 cm
10 cm =
= hyp2
8 cm √
100 = hyp2 √
? cm
10 = hyp
hypotenuse
Word Bank
Pythagorean
Theorem
right triangle
side
hypotenuse
leg
length
10 cm
Access Common Core 10 12 ? A
With which triangle could you use the Pythagorean Theorem to find the unknown length? Explain why you cannot use the Pythagorean Theorem on the other. 6 ? B
I can use the Pythagorean Theorem on Triangle A because it is a right triangle. I cannot use the Pythagorean Theorem on Triangle B because it is not a right triangle.
Summary Closure
What did you learn today about applying the Pythagorean Theorem, Distance and the Midpoint formulas to determine the Segment Length? (Pair-Share)
Use words from the word bank.