Download Geometry Name: 7.1-7.3, 9.5, Factoring, and Solving Study Guide

Geometry
7.1-7.3, 9.5, Factoring, and Solving Study Guide
Algebra Review
Find the Product.
1) 6x(x 2  2x  1)
Name: ______________________________
Period: _____ Date: ___________________
2) 4 x  1
2
Factor
3) 9x 2  64
4) y 2  10y  25
5) 2x 2  5x  3
6) x 2  5x  24
Solve by factoring.
7) 6 x 2  12 x  0
8) 3x 2  14x  8 = 0
9) x2 + 3x = 4
10) x2 – 7x = –12
Proportions
11. If
, complete the following statement:
.
12. The door in a room is 8 ft tall. An architect’s model of the same door is 2 in. high. What is the ratio
of the height of the model to the real height?
13. If a 6 ft man casts a 2.4 ft shadow, how tall would a nearby tree be that casts a shadow 12 ft long?
Solve each proportion by finding the value of the variable.
14)
16)
15)
x 1 x  4

x2 x6
17)
x6 5

1
x
Similarity
. Complete the following.
18)
__?__
19)
20) A 3-in. by 5-in. picture is enlarged so that the longer side measures 6 ft. What is the length of the
shorter side?
21) Are the polygons similar? If so, give the similarity ratio of the
first polygon to the second. If not, explain.
Are the polygons similar? If they are, write a similarity statement, and give the similarity ratio. If
they are not, explain.
22)
23)
Dilations
24) Draw the image with center E using the following transformation rule: D 1 ABC . Label the image A’B’C’.
2
25) You are given that triangle ADE ~ triangle ABC. If BC = 9, DB = 5x-6, DA = x, and DE = 3, then find x.
26) You are given that triangle ADE ~ triangle ABC. If DA = 2, DB = 5, DE = x, and BC =28, then find x.
27) What are the three ways we can prove triangles similar? Draw examples for each:
28)
Find the coordinates of the vertices of the image of ABC for the dilation with a scale factor of 3 centered
at the origin if A = (3,2) B= (-6, 5) C = (0, 9).