Victory for the ACT Student Text 15e

238 • M ATH

 –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ –Š‡ ’‡”‹‡–‡” ‘ˆ PQR T ?

 –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ ™Šƒ– ‹• –Š‡ ƒ”‡ƒ ‘ˆ MNO T ?

10.

11.

Properties of Triangles Items #10–11

A.

F. 12 3 G. 12 2 3 H. 12 4 3 J. 28 K. 56

1

Throwback to Math Class In a 30° 60° 90° triangle, the leg opposite the 30° angle equals the hypotenuse length multiplied by 2 1 ; the leg opposite the 60° angle equals the hypotenuse length multiplied by 2 3 .

2 B. 2 2 C. 1 D. 2 E. 2

Throwback to Math Class Triangles with angles measuring 45°, 45°, and 90° are right isosceles triangles with a hypotenuse equal to the length of either side multiplied by 2 .

Throwback to Math Class Remember that a triangle’s height is perpendicular to its base. Often, you won’t be given a line perpendicular to the base so you will have to sketch it in and determine the length using the Pythagorean theorem.

Throwback to Math Class The perimeter of a triangle is the sum of the lengths of its sides. The area of a triangle is equal to one-half of the base, b , multiplied by the height (altitude), h . The base and height are always perpendicular to each other:

= + +

s s s 1 2 3

Perimeter

triangle

1

bh

Area

triangle

2

RECTANGLES AND SQUARES

If the area of the rectangle below is 18, what is the perimeter? F. 9 G. 12 H. 18 J. 24 K. 30

 –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ PQRS If PR 5 centimeters, what is the area, in square centimeters, of the rectangle? A. 2 B. 3 C. 4 D. 8 E. 12 is a rectangle.

12.

13.