Book Section 7-2 Online Unit 1 Lessons 3 & 4

Instruction Pythagorean Theorem: – In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse a 2 + b 2 = c 2 a b c

Instruction Pythagorean Triple: – Set of nonzero whole numbers a, b, and c that satisfy equation a 2 + b 2 = c 2 Examples: – 3, 4, 5 – 5, 12, 13 – 7, 24, 25 Fun Fact: If you multiply each number in a Pythagorean Triple by the same whole number, the three numbers that result also form a Pythagorean Triple.

Instruction Converse of the Pythagorean Theorem: – If the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Instruction Theorem: – If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, the triangle is obtuse If c 2 > a 2 + b 2, then the triangle is obtuse

Instruction Theorem: – If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, the triangle is acute If c 2 < a 2 + b 2, then the triangle is acute

Let’s Practice Find x. a 2 + b 2 = c = c = c = c 2 10 = c

Let’s Practice Find x. Leave your answer in simplest radical form a 2 + b 2 = c b 2 = b 2 = 49 b 2 = 33

Let’s Practice Allentown is 35 miles North and 12 miles east of Philadelphia. A train runs on a straight track between the two towns. How many miles does it cover? Phil * Allentown = c = c = c 2 37 = c

Let’s Practice Find the area of the shaded region. 6 8 h a 2 + b 2 = c b 2 = b 2 = 64 b 2 = 28 A = ½ bh A = ½ (12)

Let’s Practice The lengths of the sides of a triangle are 15, 8, and 21. Is this a right, acute, or obtuse triangle? If it’s a right trianlge: a 2 + b 2 = c = = = < < c 2 OBTUSE

Review Pythagorean Theorem: a 2 + b 2 = c 2 If c 2 < a 2 + b 2, then the triangle is acute If c 2 > a 2 + b 2, then the triangle is obtuse

Follow Up Each question is worth 1 extra credit point added to your chapter 1 test Submit via webmail with subject heading “7-2 Extra Credit” 1. The lengths of two legs of a right triangle are 16cm and 30cm. What is the length of the hypotenuse? Show work 2. The length of the hypotenuse of a right triangle is 65 yards. The length of one leg is 25 yards. What is the length of the other leg? Show work 3.Which is closest to the length of the diagonal of a square whose sides measure 20 cm? Show work A.20 cm B.28cm C.40cm D.200cm 4. A ladder resting against the side of a building reaches 32ft up the building. If the ladder is 40ft long, how far from the building is the base of the ladder? Show work. 5. The following are the lengths of the sides of three triangles. TriangleSide Measurements ∆QRS9, 12, 15 ∆TUV17, 23, 31 ∆WXY28, 96, 100 Which are right triangles? Show work