Name: 

Two polygons are similar if and only if one of these conditions are
satisfied:

1. All pairs of corresponding angles are congruent.
2. All pairs of corresponding sides are proportional.

Please Refer to Unit 5.4

A Pythagorean triple is a set of three natural numbers

Please refer to Unit 5.5

Theorem 5.5.4

If the length of the hypotenuse of a right triangle is three times
the length of one leg of the triangle, then the angle of the
triangle opposite that leg measures 30°.

When two geometric figures have exactly the shape they are said to be:

When two figures have the same shape (~) and all
corresponding parts have equal (=) measures, the two
figures are

Please Refer to Unit 5.1

Find the best form of each ratio:
a) 12 to 20
b) 12 in. to 24 in.
c) 12 in. to 3 ft (Note: 1 ft = 12 in.)
d) 5 lb to 20 oz (Note: 1 lb = 16 oz)
e) 5lb to 2ft is in commensurabe!
f) 4m to 30cm

Theorem 5.4.7

Let a, b, and c represent the lengths of the three sides of a
triangle, with c the length of the longest side.

1. If c² > a² + b², then the triangle is obtuse and the obtuse
angle lies opposite the side of length c.

2. If c² < a² + b², then the triangle is acute.

Determine the type of triangle represented if the lengths of
its sides are as follows:
a) 4, 5, 7
b) 6, 7, 8
c) 9, 12, 15
d) 3, 4, 9

What kind of triangle do the figures, at the bottom, represent?

a) Choosing c = 7, we have 7² > 4² + 5², so the triangle is
obtuse.
b) Choosing c = 8, we have 8² < 6² + 7², so the triangle is
acute.
c) Choosing c = 15, we have 15² = 9² + 12², so the triangle
is a right triangle.
d) Because 9 > 3 + 4, no triangle is possible. (Remember
that the sum of the lengths of two sides of a triangle
must be greater than the length of the third side.)

Please Refer to Unit 5.6

If the ages of the children are 2, 4, and 6 (assume
exactness of ages for simplicity) and the total in the
account is $7200, then the amount that each child should
receive can be found by solving the equation

Solve this quation-2x + 4x + 6x = 7200