Geometry Section 7.1-7.2

A yellow square lays on top of a purple square A yellow square lays on top of a purple square. Find the area of the purple square behind the yellow square.

EXAMPLE 2 Standardized Test Practice SOLUTION (hypotenuse)2 = (leg)2 + (leg)2 = +

EXAMPLE 3 Find the area of an isosceles triangle Find the area of the isosceles triangle below.

EXAMPLE 4 Find the length of the hypotenuse of the right triangle.

What is the diagonal length of a TV screen whose dimensions are 80 x 60 cm?

Verify right triangles EXAMPLE 1 Verify right triangles Tell whether the given triangle is a right triangle. a. b. Let c represent the length of the longest side of the triangle. Check to see whether the side lengths satisfy the equation c2 = a2 + b2. = ? (3 34)2 92 + 152 a. b. 262 222 + 142 = ? 9 34 81 + 225 = ? 676 484 + 196 = ? 306 = 306 676 = 680 The triangle is a right triangle. The triangle is not a right triangle.

EXAMPLE 2 Classify triangles Can segments with lengths of 4.3 feet, 5.2 feet, and 6.1 feet form a triangle? If so, would the triangle be acute, right, or obtuse? SOLUTION STEP 1 Use the Triangle Inequality Theorem to check that the segments can make a triangle. 4.3 + 5.2 = 9.5 4.3 + 6.1 = 10.4 5.2 + 6.1 = 11.3 9.5 > 6.1 10.4 > 5.2 11.3 > 4.3 The side lengths 4.3 feet, 5.2 feet, and 6.1 feet can form a triangle.

EXAMPLE 2 Classify triangles STEP 2 Classify the triangle by comparing the square of the length of the longest side with the sum of squares of the lengths of the shorter sides. c 2 ? a 2 + b2 Compare c 2 with a2 + b2. 6.12 ? 4.3 2 + 5.22 Substitute. 37.212 ? 18.49 2 + 27.042 Simplify. 37.21 < 45.53 c 2 is less than a2 + b2. The side lengths 4.3 feet, 5.2 feet, and 6.1 feet form an acute triangle.