Pythagorean Theorem Distance Formula. Vocabulary Right Triangle – A Triangle with one 90° angle Hypotenuse – The longest side of a right triangle (opposite.

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Presentation transcript:

Pythagorean Theorem Distance Formula

Vocabulary Right Triangle – A Triangle with one 90° angle Hypotenuse – The longest side of a right triangle (opposite the 90° angle) Legs – The two sides of a right triangle adjacent to the 90° angle Write in Notes

Pythagorean Theorem Write in Notes

Example 4-1a Find the length of the hypotenuse of a right triangle if and Answer: The length of the hypotenuse is 30 units. Pythagorean Theorem Simplify. Take the square root of each side. Use the positive value. and

Example 4-1b Find the length of the hypotenuse of a right triangle if and Answer: 65 units

Example 4-2a Find the length of the missing side. In the triangle,andunits. Answer: To the nearest hundredth, the length of the leg is units. Pythagorean Theorem Evaluate squares. Subtract 81 from each side. Use a calculator to evaluate. Use the positive value. and

Example 4-2b Find the length of the missing side. Answer: about units

Pythagorean Triples Integers that can create a right triangle are known as Pythagorean Triples 3,4,5 5,12,13 8,15,17 7,24,25 Multiples are also triples e.g. 6,8,10 Write in Notes

Example 4-3a Multiple-Choice Test Item What is the area of triangle XYZ ? A 94 units 2 B 128 units 2 C 294 units 2 D 588 units 2 Read the Test Item The area of the triangle isIn a right triangle, the legs form the base and height of the triangle. Use the measures of the hypotenuse and the base to find the height of the triangle.

Example 4-3a Solve the Test Item Step 1Check to see if the measurements of this triangle are a multiple of a common Pythagorean triple. The hypotenuse isunits and the leg isunits. This triangle is a multiple of a (3, 4, 5) triangle. The height of the triangle is 21 units.

Example 4-3a Step 2Find the area of the triangle. Answer: The area of the triangle is 294 square units. Choice C is correct. Area of a triangle and Simplify.

Example 4-3b Multiple-Choice Test Item What is the area of triangle RST ? A 764 units 2 B 480 units 2 C 420 units 2 D 384 units 2 Answer: D

Example 4-4a Determine whether the side measures of 7, 12, 15 form a right triangle. Answer: Since, the triangle is not a right triangle. Pythagorean Theorem Add. and Multiply. Since the measure of the longest side is 15, let, and Then determine whether

Example 4-4b Determine whether the side measures of 27, 36, 45 form a right triangle. Pythagorean Theorem and Multiply. Since the measure of the longest side is 45, let and Then determine whether Add. Answer: Sincethe triangle is a right triangle.

Determine whether the following side measures form right triangles. a. 33, 44, 55 b. 12, 22, 40 Example 4-4b Answer: right triangle Answer: not a right triangle

Homework 11-4 Pythagorean Theorem Even Use time left in class to work on homework

Homework Quiz