Page 238 - Algebra 1

L E S S O N Writing and Solving Proportions 36
Warm Up
New Concepts
1. Vocabulary A is a comparison of two quantities using (31) division.
Solve.
2.13= x 3.42=63 __ __
(31) 52 36
4. 15x - 37 = 143
(23)
(31) 56 w
5. 78 + 22y = -230
(23)
Proportions are frequently used to solve problems in mathematics. Proportional reasoning can be applied in many situations, including reading and drawing maps, architecture, and construction. Solving problems in these situations requires knowledge of similar figures.
If two geometric objects or figures are similar, they have the same shape but are not necessarily the same size. The triangles below are similar.
Reading Math
The ∼ symbol indicates similar figures and reads “is similar to.”
The symbol indicates congruent figures and reads “is congruent to.”
B
12
A 5 C D 2.5 F
ΔABC ∼ ΔDEF
When two figures are similar, they have sides and angles that correspond. Corresponding sides and angles are found using the order of the letters in the similarity statement. In the triangles above, ∠A and ∠D correspond, ∠B and ∠E correspond, and ∠C and ∠F correspond. Corresponding angles of similar figures are congruent, or have the same measure.
∠A ∠D ∠B ∠E ∠C ∠F
−−
and DE correspond, BC and EF correspond, and AC and DF correspond. Corresponding sides of similar figures do not have to be congruent. However, they do have to be in proportion. The ratio of the all pairs of corresponding sides must be the same.
AB _
24
E
Sides of similar figures also correspond. In the example above, AB −− −−−− −−−−
Reading Math
−−
AB is read “segment AB.”
DE = EF = DF
In the example above, the ratio of the sides of ΔABC to ΔDEF is 2 to 1.
BC _
AC _
This ratio, which can also be written as _2 or 2:1, is called the scale factor of
1
AB = BC = AC = _2
A scale factor is the ratio of a side length of a figure to the side length of a similiar figure. The scale factor of ΔDEF to ΔABC is 1 to 2.
ΔABC to ΔDEF.
___
DE EF DF 1
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Lesson 36 223