Module A2 – The Coordinate Plane
Lesson 1 - page 1
Title: Pythagorean Theorem and Distance
Duration: 2-3 days
I. Before Engagement
Knowledge & Skills
o
o
o
o
Understand language related to right triangles
Apply the Pythagorean Theorem in order to solve problems involving unknown side lengths of right triangles
Understand operations and labeling within a coordinate system
Apply the Pythagorean Theorem in order to find the distance between two points in the coordinate system
Vocabulary for Student Discourse
Coordinate System
Hypotenuse
Pythagorean Theorem
Right Triangle
Leg
Distance
II. Evidence of Individual Sense-Making
Text: McDougal-Littell’s Geometry Concepts and Skills
Section 4.4 (The Pythagorean Theorem and the Distance Formula)
20-22, 26, 37
Explain your process
28, 31 & 32
If not congruent – identify the longer segment and state how much longer.
Additional Problems:
1. If a window washer wants to reach a second story window that is 14 feet above the ground, can he place his
17 foot ladder 8 feet away from the base of the building? Explain your answer.
2. Rita’s front door is 42” by 84”. She needs to bring in a 96” diameter table top. Will she be able to fit this
through her door? Explain your answer.
3. Triangle DEF has coordinates D(-2,-3), E(1,1) and F(-1,4). What is the perimeter of triangle DEF?
4. Two birds are flying toward a feeder located at F(5,10). A cardinal is coming
from C(10,-2) at a rate of 20 miles per hour and a sparrow is coming from S(4,4) at a rate of 16 miles per hour. Which bird will reach the feeder first if the
units on the coordinate plane are in miles?
39.
Describe and correct the error in using the Pythagorean Theorem:
a)
b)
Geometry – CCSSM
Module A2 – The Coordinate Plane
Lesson 1 - page 2
GeoGebra Activity: Pythagorean Theorem
Step 1
⃡ . Draw a line perpendicular to 𝐴𝐵
⃡ through A. Label a point C on the perpendicular line.
Draw and label 𝐴𝐵
Step 2
̅̅̅̅ .
Draw 𝐵𝐶
Step 3
Measure AB, AC and BC
Geometry– CCSSM
Module A2 – The Coordinate Plane
Lesson 1 - page 3
Step 4
Find the values of (𝐴𝐵)2 , (𝐴𝐶)2 𝑎𝑛𝑑 (𝐵𝐶)2
Step 5
Find the value of (𝐴𝐵)2 + (𝐴𝐶)2
Geometry– CCSSM
Module A2 – The Coordinate Plane
Lesson 1 - page 4
Collaborative Activity: Distance Formula to Decode a Message
Materials:
graph paper, paper, pencil, calculator
In this activity, your group will apply the Distance Formula to encode and decode messages hidden in a
coordinate plane. A sample message is shown.
Instructions:
1. Use graph paper to make a coordinate plane. Graph and label enough points to spell out a math
word or short phrase. (Every letter in the word or phrase should have its own point.)
2. On separate paper, write the coordinate of each point and calculate the distance between each of
the letters in the message. Make sure that no two points are the same distance apart.
3. Encode the message by writing the distances in order and identifying a starting point.
4. Exchange the encoded message with another group. Decode the other group’s message, showing
the calculation for each distance.
Analyzing the results:
1. Did your group have to use the distance formula to find all of the correct points? Explain.
2. Describe the strategy your group used to find the consecutive points in the message.
Geometry– CCSSM
Module A2 – The Coordinate Plane
Lesson 1 - page 5
Guided Practice Problems
1. You are hiking on a trail that lies along a straight railroad track. The total length of the trail is 5.4
kilometers. You have been hiking for 45 minutes at an average speed of 2.4 kilometers per hour.
How much farther (in kilometers) do you need to hike to reach the end of the trail?
̅̅ are 𝐿(−2,2) and F(3,1). The endpoints of ̅̅̅
2. The endpoints of ̅̅
𝐿𝐹
𝐽𝑅 are J(1, −1) and R(2, −3). What
is the approximate difference in the lengths of the two segments?
Geometry– CCSSM