Warm-Up 1
Day 9: Geometry and Pythagorean Theorem
Review geometry ideas and preview right triangle reasoning.
Student Goal
I can use geometry ideas to solve problems with shapes and distance.
Why It Matters
Geometry and right triangle reasoning help students understand distance, design, coordinate grids, and 8th grade problem solving.
Warm-Up
Warm-Up 2
On a grid, how far is it from (2, 3) to (7, 3)?
Warm-Up 3
Which side is longest in a right triangle?
Short Lesson
Standard Focus
NC.8.G: Geometry
Student-Friendly Standard Goal
I can reason about right triangles, distance, and simple geometric relationships.
- A right triangle has one 90 degree angle.
- On a coordinate grid, horizontal and vertical movement can form the legs of a right triangle.
- The Pythagorean Theorem connects the side lengths of a right triangle: a^2 + b^2 = c^2.
Guided Examples
Guided Example 1
Distance on a Grid
A point moves from (1, 2) to (5, 2), then to (5, 5). What are the two leg lengths?
Step 1
from (1,2) to (5,2)
What is the horizontal distance?
Guided Example 2
Use the Pythagorean Theorem Preview
A right triangle has legs 6 and 8. What is the hypotenuse?
Step 1
6^2 + 8^2 = c^2
What is 6^2 + 8^2?
Practice
Problem 1
Which triangle side is across from the right angle?
Problem 2
Find the vertical distance from (4, 1) to (4, 9).
Problem 3
A right triangle has legs 5 and 12. Which equation helps find the hypotenuse?
Problem 4
True or false: The Pythagorean Theorem is used with right triangles.
Problem 5
A ladder, wall, and ground form a right triangle. The ladder is across from the right angle. What is the ladder?
Reflection
How are you feeling about today's skill?
Optional reflection: Where might distance and right triangles show up in real life?