Lesson 35: Special Right Triangles and the Pythagorean Theorem

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Presentation transcript:

Lesson 35: Special Right Triangles and the Pythagorean Theorem Texas Algebra I Lesson 35: Special Right Triangles and the Pythagorean Theorem

Lesson objectives: The student will be able to: Use the Pythagorean theorem to find the missing length of a side of a right triangle. Identify and use the relationships of 30-60-90 and isosceles right triangles Identify Pythagorean “triples”

Pythagorean Theorem The sum of the square of the legs, a and b, of a right triangle is equal to the square of hypotenuse, c. Algebraically expressed: a² + b² = c² Huh? Okay, let’s look at a picture!

Classic Pythagorean Proof

Special Right Triangles Pythagorean Triples All 3 side lengths are whole numbers Any ratio of triples will work! Examples: 3-4-5 5-12-13

Special Right Triangles Isosceles right 45-45-90 Legs congruent Hypotenuse length is equal to the length of the leg ×√2

Special Right Triangles 30-60-90 Half of an equilateral triangle Shortest leg half the length of the side of the equilateral Longer leg is equal to the length of the short leg ×√3

Practice Problems The figure is a parallelogram. Find the missing length:

Practice Problems Find the missing length:

Lesson objectives: The student will be able to: Use the Pythagorean theorem to find the missing length of a side of a right triangle. Identify and use the relationships of 30-60-90 and isosceles right triangles Identify Pythagorean “triples”