geometry semester 1 name: final exam...

Geometry Semester 1 Name:__________________________ Final Exam Review

1) Complete each sentence with the appropriate vocabulary word from the word bank below. You will not use some of the words. Do not use a word more than once!

a. b. c. d.


e. f. g. h.


2) Fill in the blank for the questions below (a.)

AD is a(n) __________________ of △ABC (b.)

AC is a(n) __________________ of △ABD

(c.)

DE is a(n) __________________ of △ABD


3) Draw a circle and label its center point A. Draw and label point B anywhere outside the circle.

Draw two segments from point B that are tangent to opposite sides of the circle. Draw a radius

to each point of tangency.

What shape did you draw? __________________

4) Given: O is the midpoint of JY

OJ = 3x + 7

OY = 4x + 1

Find : x=___________ JY=____________

5) Given : JUI = 41

LUI = 3y + 7

JUL = 87

Find: y=___________

J Y O

U

J

I

L


6. Use the triangle below to find the m∠T

7) Mike wants to build a triangular playpen for his pet kangaroo. He’s already purchased two sides for this pen: one side measures 25 ft, and the other measures 45 ft. He needs to purchase the correct size for the third length. What is the range of possible lengths for the third side of his play pen?

8) ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹. 𝐴𝐵 = 3𝑥 − 1, 𝐵𝐶 = 2𝑥 + 10, 𝐴𝐶 = 𝑥 + 6, 𝐸𝐹 = 4𝑥 − 20

Solve for x = _________________, EF = ___________, perimeter of ∆𝐷𝐸𝐹 = _____________


9 Decide whether it is possible to prove that the triangles are congruent. If it is possible, tell

which congruence postulate or theorem you would use.

10.)Mark the each diagram appropriately. Then, complete the congruence statement.

ΔBAD ≅ Δ________ by ______ ΔEFG ≅ Δ________ by ______

C

B

D

A

E H

G is the midpoint of

G

H

E F

I


CA

B

D

11.) Mark the diagram and write a proof.

Options include

Two Column

Flow Chart

Paragraph

Statement Reason

AB BC

Given

BD bisects ABC

Given

ABD CBD

Definition of angle bisector

BD DB

Reflexive Property (shared side)

ABD CBD

SAS

AD DC

CPCTC

Given: AB BC

BD bisects ABC

Prove: AD DC


12 Find the value of x.

13. Find the value of x.

x + ½x + 15 = 180 2x + 5 + 6x + 15 = 180

1.5x = 165 8x + 20 = 180

x = 110 x = 20

4x + 3x + 40 = 180 7x = 140

x = 20

8x + 5 = 2x + 11 6x = 6

x = 1


2

1

L

K J

GH

I

14) Given: 1 2 Which conclusion about the diagram must be TRUE?

A. GH||IJ

B. GI||HJ

C. GK||LJ

D. LJ||HJ

15) a. Given: 3 2

Which two lines must be parallel? _____ || _____

How do you know?

b. Given: 1 2

Which two lines must be parallel?

_____ || _____ How do you know?

A

G

D

F

H

E

C

B

1

2

1 2

3 4

A B

C D


50 68

74

R

P

A

L

16) Find the value for x that makes line p and line q

parallel.

17) Find one possible value for x that makes line p and line q not parallel. 18) PARL is a parallelogram with a perimeter of 250 units. Find the missing information

m R = _______

mALR = _______

PA = _______

mLAR = ________

19) Decide whether the following statements are true or false.

a) A kite always has perpendicular diagonals.

b) A rectangle always has congruent diagonals.

c) A parallelogram always has congruent diagonals.

d) A trapezoid’s diagonals always bisect each other.

e) A parallelogram’s diagonals always bisect each other.

f) A kite always has two pairs of congruent sides.

g) A parallelogram always has two pairs of congruent sides.

h) A trapezoid always has two pairs of congruent sides.

135o

(13x-10)°

p

q

r


20) Find m ORE .

21) a) If ABC is isosceles with base AB , 7 9m A x , and 12 31m B x ,

find m C .

b) If ABC is isosceles with base AB , and 57m C . Find the measure of the supplement of B .

R

O S

E

40°


22) Solve for x

23) To quickly get from the Farmer’s Market to the Evanston Library by bike, you must ride 2 blocks east, 1 block south, another 3 blocks east and 5 more blocks south. What is the actual distance between the Farmer’s Market and the Library?

24) In the diagram, if a = 14 feet, find the exact values of x, b and c.

x = __________

b = __________

c = __________

25) Find the distance between the following two points: (-33, 65) and (3, -14).

__________________


26) Find the area of the following figures below

27) Given following points: A=(2,1) B=(8, 1) C=(8, 8) D=(2,3)

Find the area of the shape.

28) Find the area of the shape.

_

6

_

11

_

13

_

_

5

_

(12,0)

_

(3,24)

_

(3,8)

_

C

_

B

_

D


29) Find the area of the following shape in two different ways. Assume right angles.

30) Find the area of the following shapes:

a) AC = 6 cm. DH =4 cm. BH = 9 cm.

b)

15 ft.

5 ft.

12 ft. 9 ft.

A

B

C

DH


c) d)

31) Walter is a making a picture frame for a 5 in.-by-7 in.

picture centered in a 10 in.-by-12 in. frame. He wants to

cover each trapezoidal piece of wood with gold

leaf before putting the frame together. How

many square inches of gold leaf will he need to cover

the frame?

13

24


32) SELECT JUST ONE OF THESE PROBLEMS TO DO!!! Choice #1: A rectangular swimming pool is 30’ by 42’. A 3 foot concrete walkway is placed all around the pool. Find the area of this walkway. Show your calculations. Choice #2: ABCD is a “tilted” square. A = (10, 15) B = (16,11) Find the exact area of this square. Show your calculations.

33) Find the area of the triangle enclosed by these three lines:

2x 3y 48

x-axis y-axis You must make a sketch of the triangle and show all your calculations.

geometry semester 1 name: final exam...

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