Josh has taught Earth Science and Physical Science at the High School level and holds a Master of Education degree from UNC-Chapel Hill.
After this lesson, students will be able to:
- define right triangle.
- perform several different calculations based on theorems and proofs of right triangles.
30 - 60 minutes
Explain a proof of the Pythagorean Theorem and its converse.
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
- Measuring tape
- Begin the lesson by drawing or displaying a right triangle on the board. Ask students to make observations of the shape. Write these observations on the board.
- Start the video lesson Properties of Right Triangles: Theorems & Proofs. Pause the video at 3:02.
- Write the Pythagorean Theorem on the board. Provide a few sample problems for students to solve and circulate around the room to provide assistance as they do so.
- Next, ask for student volunteers to measure the room using a measuring tape. Students will use these measurements to calculate the length of the hypotenuse formed by two adjacent walls of the classroom.
- Using the measurements taken by the student volunteers, have students work out the hypotenuse measurement on their own. Then, have them pair up to compare answers and provide feedback to each other. Ask for a volunteer pair to share their answer and walk through the problem as a class. Now, ask for a student volunteer to measure the hypotenuse directly to verify students' answers.
- Resume the video. Pause it again at 4:32. Write the formula for the altitude of a right triangle on the board and work through a few sample problems, allowing students to try them on their own first, just as before.
- Next, mark on the floor approximately where the altitude of the right triangle measured previously would land. Have a student measure one section of the hypotenuse (and thus, determine the other) in order to allow all the students to calculate the altitude. Repeat the same process as before.
- Resume and finish the video. Ask for a pair of student volunteers to measure the median of the room's right triangle to verify the concept behind the median.
Right Triangle Word Problems Activity
- Now that students have an understanding of the various properties of right triangles, they will create word problems to share with their classmates for practice.
- Ask each student to write two distinct word problems in which a real-world scenario uses the properties of a right triangle to measure something. The goal here is to be creative while applying the concepts learned in the lesson.
- Students can swap their word problems (as many times as you'd like) and practice solving them.
- As an exit ticket, students can complete the associated quiz.
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