Download Geometry 2NW Study Guide 2014-15

2014-2015
Geometry
Second Nine Weeks Study Guide
1.
Which lines are //? Justify.
a
1200
550
b
c
0
60
1000
2.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
d
Give the Symbolic form of the following:
Conditional statement ______
Contra-positive Statement______
Converse Statement______
Inverse Statement_______
Conjunction______
Disjunction_______
Therefore________
Law of detachment
Law of syllogism
Law of contra-positive
3.
What determines if lines are parallel?_______________________________________________
4.
How do you prove triangles are Congruent?__________________________________________
5.
How do you prove triangles are similar?_____________________________________________
6.
If you are given two sides of a triangle, how do you determine the length of the third side?
__________________________________________________________________________
Use the following points for questions 7-12.
A( -6, -2) and T( 1, -9)
̅̅̅̅. __________________________________________________
7.
Find the distance of the 𝐴𝑇
̅̅̅̅
8.
Find the midpoint of 𝐴𝑇.______________________________________________________
̅̅̅̅._________________________________________________________
9.
Find the slope of 𝐴𝑇
̅̅̅̅.____________________________________________
10.
Find the slope of a line parallel to 𝐴𝑇
11.
Find the slope of a line perpendicular to ̅̅̅̅
𝐴𝑇._______________________________________
̅̅̅̅. Find the integral coordinate for Z.___________________________
12.
If T is the midpoint of 𝐴𝑍
13.
Name all the angle pairs and the relationships you can use to ensure a//b .
8 1
7 2
a
3 6
4
5
b
Use your answers to question 4 to answer questions 14-16.
14.
Given: ̅̅̅̅
𝐴𝐵 ∥ ̅̅̅̅
𝐶𝐷 What would prove ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐷𝐵? ____________________________
A
15.
B
D
C
̅̅̅̅ ∥ 𝐷𝐸
̅̅̅̅ What would prove ∆𝐴𝐵𝐶 ≅ ∆𝐸𝐷𝐶?_____________________________
Given: 𝐴𝐵
A
C
D
B
E
16.
Given: ∠𝐵 ≅ ∠𝐷 What would Prove ∆𝐴𝐵𝐶 ≅ ∆𝐸𝐷𝐶?_____________________________
A
B
17.
C
D
Fill in the Blanks for the proportional parts of the following Diagram if ∆𝐴𝐵𝐶~∆𝐸𝐵𝐷.
̅
̅̅̅̅ 𝐶𝐵
̅̅̅̅
𝐴𝐵
=
=
̅
̅̅̅̅
̅̅̅̅ A
𝐸𝐵
𝐸𝐷
D
B
C
E
D
A
18.
AC = 3, ED = 9, AB = 4, EB = _________
19.
Is ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹? ________
B
C
E
B
5
A
10
6
7
C
12
F
20.
E
D
14
In ∆𝑋𝑌𝑍 ∠𝑋 = 83° 𝑎𝑛𝑑 ∠𝑌 = 42° List the sides in order from longest to shortest._______________________
̅̅̅̅ = 15, ̅̅̅̅
21.
In ∆𝑋𝑌𝑍 𝑋𝑌
𝑌𝑍 = 19, 𝑎𝑛𝑑 ̅̅̅̅
𝑋𝑍 = 11. List the angles in order from smallest to
largest.________________________
22.
Would 9.8, 5.1 and 4.7 form a triangle?__________________
̅̅̅̅ ≅ 𝐶𝐹
̅̅̅̅ , 𝐶𝐷
̅̅̅̅ ≅ ̅̅̅̅̅
23.
Given 𝐴𝐶
𝐶𝐵 What would prove that ∆𝐶𝐴𝐷 ≅ ∆𝐶𝐹𝐵?______________________
A
B
E
C
F
D
24.
On a map Richmond, Virginia Beach and Suffolk form a triangle. Richmond to Virginia beach is 140 miles,
Virginia Beach to Suffolk is 50 miles. What is the possible distance from Richmond to Suffolk?
25.
Given the statement: If I ride my bike, then I will be in shape. Write the following statements.
a.
b.
c.
d.
Converse:_______________________________________________________________
Inverse:_________________________________________________________________
Contrapositive:___________________________________________________________
Biconditional:_____________________________________________________________
26.
Given the 𝑚∠𝐴 = 4𝑥 + 8 𝑎𝑛𝑑 𝑚∠𝐵 = 𝑥 + 1. If the angles are compliments of each other find the measures of
the two angles.
27.
Given the 𝑚∠𝐴 = 4𝑥 + 8 𝑎𝑛𝑑 𝑚∠𝐵 = 𝑥 + 1. If the angles are supplements of each other find the measures of
the two angles.
Use the diagram below to answer questions 28 and 29.
431 Cell Phone Subscribers
AT&T
208
Verizon
10 158
28.
29.
(All, Some, None) Subscribers belong to AT&T and Verizon.________
How many customers do not subscribe to AT&T and Verizon?_______
30.
Given: ∆𝐴𝐵𝐶 ≅ ∆𝐸𝐹𝐺 Find the value of X._________________
B
2x+5
E
3x
x+4
30
A
6x
C
G
2x-1
F
̅̅̅̅ = 5 𝑎𝑛𝑑 ̅̅̅̅
̅̅̅̅ if 𝐴𝐶
̅̅̅̅ represents the hypotenuse.
31.
If ∆𝐴𝐵𝐶 𝑖𝑠 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝐴𝐵
𝐴𝐶 = 13. Find the length of 𝐵𝐶
________________________
W
32.
Fill in the blanks for the following Proof:
Given: 𝑌𝑈 ∥ 𝑊𝐻
Prove: ∆𝑌𝑂𝑈~∆𝐻𝑂𝑊
Y
O
U
H
Statements
1. 𝑌𝑈 ∥ 𝑊𝐻
2.∠𝑈𝑌𝑂 ≅ ∠𝑊𝐻𝑂
3.
4. ∆𝑌𝑂𝑈~∆𝐻𝑂𝑊
Reasons
1.
2.
3.Vertical Angles
4.
A
B
33.
Fill in the blanks for the following proof:
Given: 𝐴𝐵 ∥ 𝐷𝐶 𝑎𝑛𝑑 ∠𝐴 ≅ ∠𝐷
Prove: ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐶𝐵
C
Statements
1. : 𝐴𝐵 ∥ 𝐷𝐶
2. ∠𝐴𝐵𝐶 ≅ ∠𝐷𝐶𝐵
3. ∠𝐴 ≅ ∠𝐷
4.
5. : ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐶𝐵
34.
D
Reasons
1.
2.
3.
4.Reflexive property
5.
̅̅̅̅ with A(-2, 5) and B(4, -2). Write the equation of circle P.
Given the Diameter of circle P is 𝐴𝐵
35.
Given: The Equation of the circle is (𝑥 + 5)2 + (𝑦 − 3)2 = 169. Name the center of the circle and the radius
of the circle.
36.
Fill in the missing angle measures, given line sand line t are parallel.
37.
Given line s//t. Solve for x.
a. m∠4 = 77o and 𝑚∠8 = (4x + 57)o
b. 𝑚∠3 = (5x + 13)o and 𝑚∠5 = 53o
c. 𝑚∠1 = (6x – 5)o and 𝑚∠7 = 115o
38.
39.
Identify each pair of angles as corresponding, alternate interior, alternate exterior, or consecutive interior.
Solve for the missing angle measures.
X
y
40.
Fill in the missing angles.
95o
115o
41.
Draw a construction for the bisector of an angle and a perpendicular bisector of a line segment.
Technology Enhanced Items
Directions: Shade the box to choose each value you want to select.
You must select all correct values.
42. In triangle ABC, side 𝐴𝐵 is 15cm and side 𝐵𝐶 is 21cm. What are the possible side lengths of side 𝐴𝐶 ?
36 cm
40 cm
14 cm
56.5 cm
17 cm
35 cm
Directions: Write your answer in the box.
43. In the triangle below, find the value of x.
(3𝑥 + 10)°
(5𝑥 − 15)°
1
( 𝑥 + 15)°
2
Directions: Select the correct side for each box using the bank below.
44. For the triangle below, list the side length in order from smallest to largest.
B
31°
A
SIDES
85°
𝐴𝐵
64°
C
𝐵𝐶
𝐴𝐶
Directions: Complete the proof by filling in the blanks. Select the correct answer for each box using
the bank.
45. Given: B is the midpoint of 𝐴𝐶 , 𝐴𝑀 ≅ 𝐵𝑁, and 𝐴𝑀 || 𝐵𝑁.
Prove: ∆ABM ≅ ∆BCN
C
B
N
A
M
Statements
Reasons
1. B is the midpoint of 𝐴𝐶 , 𝐴𝑀 ≅ 𝐵𝑁, and 𝐴𝑀 || 𝐵𝑁.
1. Given
2. 𝐴𝐵 ≅ ________
2. Definition of Midpoint
3. 𝐶𝐵𝑁 ≅ 𝐵𝐴𝑀
3. __________________________
4. ∆ABM ≅ ∆BCN
4. __________________________
Alternate
Interior Angles
SSS
𝐵𝐶
SAS
𝐵𝑀
𝐴𝑀
Corresponding
Angles
Directions: Complete the proof by filling in the blanks. Select the correct answer for each box using
the bank.
46. Given: 𝐶𝐴 ≅ 𝐹𝐴 and 𝐵 ≅ 𝐷
Prove: ∆ABC ≅ ∆ADF
A
F
C
D
B
Statements
Reasons
1. 𝐶𝐴 ≅ 𝐹𝐴 and 𝐵 ≅ 𝐷
1. Given
2. 𝐴 ≅ 𝐴
2. _____________________________
3. ∆ABC ≅ ∆ADF
3. _____________________________
SSS
SAS
AAS
ASA
Alternate
Interior Angles
Reflexive
Property
Vertical Angles
Theorem