1. Geometry
Section

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.

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

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

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

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

9. 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. = ?
( ) a. b. = ? = ? = ?
306 = 306
676 = 680
The triangle is a right triangle.
The triangle is not a right triangle.

11. 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.
= 9.5
= 10.4
= 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.

12. 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 ?
Substitute. ?
Simplify.
37.21 <
c 2 is less than a2 + b2.
The side lengths 4.3 feet, 5.2 feet, and 6.1 feet form an acute triangle.