Reviewing the Pythagorean Theorem

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SWBAT apply the Pythagorean Theorem and its converse to find the length of a side of a right triangle or to determine whether or not a triangle is right. Students will understand the meaning of the Pythagorean Theorem and its converse in terms of the areas of squares constructed on the sides of a triangle.

Big Idea

The focus is on student questions as we review homework and summarize with notes.

Lesson Open

8 minutes

The warm-up prompt for this lesson asks students to make a conjecture about the relationship between the areas of shapes drawn on the sides of a right triangle.  Students may posit that the areas are in the same relationship as the areas of squares drawn on the sides of a right triangle, even though the shapes are not squares.  (The shapes are similar, however, in proportion to the sides of the right triangle, so the combined area of the shapes constructed on the legs is, in fact, equal to the area of the shape drawn on the hypotenuse.)  The purpose of this rather whimsical problem is to get students to think about the Pythagorean Theorem in terms of area. 

The lesson open follows our Team Warm-up routine.  I choose students at random to write the team's answer on the board.  

I display the agenda and learning targets for the lesson.  Today, we will review homework and summarize the Pythagorean Theorem.

Homework Review

20 minutes

We use the Team Homework Review variation of our review of Area Relationships Homework Set 1.


Summarizing the Pythagorean Theorem

15 minutes

Using Guided Notes we summarize the Pythagorean Theorem, its converse, and the Hypotenuse-Leg Congruence Theorem, which students proved for homework.  Follow the link to my Strategies folder to see how I use guided notes to teach.

If there is time, I tell a very bad joke, with the punch line, "The right angel is across from the hippopotamus, with a leg on either side."  To help students remember the vocabulary.





10 minutes

If there is still time, I use the problem sets in the slide show for extra practice.  I ask students to get individual White Boards, rags, and dry erase markers.  I display the problems using the slide show, and students practice using the Pythagorean Theorem and its converse.    

Each slide has two problems, which are more or less parallel.  Students may choose to work either one. Students who are working quickly should work both, while I help those who need it.


Lesson Close and Homework

5 minutes

The lesson close follows our Individual Size-Up Routine routine.  The prompt asks students to explain why the Pythagorean Theorem is about area.


For  homework, I assign problems #1-3 of Homework Set 2 for this unit.  Problem #1 gives students a chance to use the Pythagorean Theorem to solve a real-world problem.  Problems #2-3 ask students to review transformations, which they will use in the next lesson to compare and relate the areas of two shapes.