Download Introduction to Geometry – Study Guide

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Introduction to Geometry – Study Guide
Section 1 – Scale and Scale Factor
1. On a map of the United States, ¾ inch represents 212 miles.
a. If Fatfeesch and Fatpandas are 3 ½ inches apart, how many miles apart are they?
b. If Madison, NJ and Orlando, FL are 1,073 miles apart, how many inches apart are they?
2. You are given a square whose side length is 5 inches.
a. What is the area of the square?
b. What is the perimeter of the square?
The square is then reduced by a scale factor of ½ .
c. What is the area of the new square? How does this area relate to the scale factor?
d. What is the perimeter of the new square? How does this area relate to the scale factor?
3. You are given a rectangular prism with a length of 3 inches, width of 5 inches and depth of 5 inches.
a. What is the volume of the prism?
The prism is then enlarged by a scale factor of 4.
b. What are the dimensions of the enlarged prism?
c. What is the volume of the enlarged prism?
d. How many of the original prisms could fit inside the new, enlarged prism?
e. What is the relationship between the original volume, scale factor and new volume?
4. What is the scale factor from polygon A to polygon B?
a.
A
b.
B
2.5 cm
A
B
12 cm
4 cm
7 cm
Section 2 – Congruent Figures
5. Given ∆ABC  ∆DEF:
a. Name three pairs of corresponding, congruent sides.
b. Name three pairs of corresponding, congruent angles.
6. In the diagram on the right, ∆MKL  ∆JET.
Complete the statements that follow:
a. L  _______
b. mM = _______
̅̅̅̅̅  _______
c. 𝑀𝐾
d. mT = _______
e. ML = ________
f. ∆ETJ  ___________
Section 3 – Similar Figures
7. At 3pm, a given building casts a 45 foot shadow. At the same time a 20 foot tree casts an 8 foot
shadow. To the nearest tenth of a foot, find the height of the building.
8. You have a 3.5 inch tall by 5 inch wide photograph that you want to enlarge as a gift. If the new height
of the photograph is 15 inches, what is its new width?
9. Write proportions in each of the problems below to find the length of the unknown side.
a.
b.
c. ∆ABC ~ ∆ADE
d. ∆LMN ~ ∆XYZ
Find the length of YX.
Sections 4 and 5 – Angle Relationships
10. Define each term below. Then, draw a diagram to represent the term.
Complementary angles –
Supplementary angles –
Vertical angles –
Adjacent angles –
11. Angles 1 and 2 are complementary angles. If m 1 = 42, what is the m 2?
12. Angles 1 and 2 are supplementary angles. If m 1 = 42, what is the m 2?
13. Angles 1 and 2 are vertical angles. If m 1 = 42, what is the m 2?
14. Find the value of x in each situation below:
a.
b.
15. Find the measure of angle DEG and the measure of angle GEF.
Section 6 – Angle Relationships and Triangles
16. Find the value of x and y in the diagrams below:
a.
y 128
122
x
b.
22
x
75
y
Answer Key
1.
1
a. 989 3 miles apart
b. 3.8 inches apart
2.
a.
b.
c.
d.
25 in2
20 in
6.25 in2 – Original Area (scale factor2) = New area
10 in – Original perimeter (scale factor) = New perimeter
a.
b.
c.
d.
e.
75 in3
12 inches x 20 inches x 20 inches
4800 in3
64 of the original prisms could fit in the enlarged prism
75 in3 (scale factor3) = 4800 in3
3.
4.
a. 2.8
1
b. 3
5.
̅̅̅̅  𝐸𝐹
̅̅̅̅  𝐹𝐷
̅̅̅̅ ; 𝐶𝐴
̅̅̅̅
a. ̅̅̅̅
𝐴𝐵  ̅̅̅̅
𝐷𝐸 ; 𝐵𝐶
b. A  D ; B  E ; C  F ;
6.
a. L  T
b. mM = 85
c. ̅̅̅̅̅
𝑀𝐾  ̅̅̅
𝐽𝐸
d. mT = 63
e. ML = 6 cm
f. ∆ETJ  ∆KLM
7. 112.5 feet
8. About 21.4 inches
9.
a.
b.
c.
d.
50
40
4
18
6
𝑥
= 20 ; x = 25
9
= 𝑥 ; x = 40.5 m
2
=𝑥;x=4
12
24
18
8
= 𝑥 ; x = 6 feet
10.
Complementary angles – two angles whose angle measures add up to 90°
Supplementary angles – two angles whose angle measures add up to 180°
Vertical angles – two opposite, congruent angles that share a vertex ; formed by intersecting lines
Adjacent angles – two angles who share a side and a vertex
11. 48°
12. 138°
13. 42°
14.
a. 6x + 19 + x = 180 ; x = 23
b. 78 = 5x – 2 ; x = 16
15. 6x + 4x = 90 ; mDEG = 54°, mGEF = 36°
16.
a. my = 52° ; mx = 70°
b. my = 53° ; mx = 37°