4.8 Right Triangle Trigonometry
The Pythagorean Theorem
I.SectionObjectives
- Identify and employ the Pythagorean Theorem when working with right triangles.
- Identify common Pythagorean triples.
- Use the Pythagorean Theorem to find the area of isosceles triangles.
- Use the Pythagorean Theorem to derive the distance formula on a coordinate grid.
II.MultipleIntelligences
- This lesson uses the Pythagorean Theorem in several different ways.
- You can differentiate this lesson by expanding each of the examples in the lesson.
- Begin by drawing and labeling the parts of right triangle. Be sure that students understand which are the legs
and the hypotenuse. - Prove the Pythagorean Theorem
- Start with a right triangle.
- Construct the altitude
- Use it in an example.
- Start with an example where the hypotenuse is missing.
- Ask students to use the Pythagorean Theorem to find the length of the hypotenuse.
- Example: leg 1= 4 ,leg 2= 6
- Answer−c= 7. 2
- Be sure that students understand that they will probably need to round to the nearest tenth.
- Move to finding a missing side length.
- Example, leg 1=a,leg 2= 4 ,hypotenuse= 5
- Have students solve this for leg a.
- Answer is 3.
- Introduce the concept of a Pythagorean Theorem. Show the difference between the first example where we
did not have a perfect square and needed to round, and the second example where our answer was a perfect
square. - Return to the text and demonstrate the other Pythagorean Triples.
- Move on to finding the area of an isosceles triangle.
- Walk through this example in the text.
- Complete the exercise on the board step by step.
- Then allow time for student questions.
- Intelligences- linguistic, logical- mathematical, visual- spatial, interpersonal
III.SpecialNeeds/Modifications
- Review constructing an altitude.
- Review symbol for similar.
- Review finding square roots/radicals.
4.8. Right Triangle Trigonometry