Semester 1 Exam Review Name: Geometry Geometry Sem 1 Final ...rohls.weebly.com/uploads/2/8/2/1/2821453/geo_sem_1_final_exam... · Semester 1 Exam Review Name: _____ Geometry 11) Find

Semester 1 Exam Review Name: ___________________________________ Geometry

Geometry Sem 1 Final Review Draft

1) Using transformations, show that a||b

2) Find the measure of the numbered angles.

m 1 = ___________

m 1 = ___________

m 1 = ___________

m 1 = ___________ m 2 = ___________ m 3 = ___________ m 4 = ___________

3) Given a || b cut by a transversal c, which of the following statements is not true.

A) 1 and 3 are corresponding angles B) 2 and 3 are same-side int. angles C) 3 and 4 are vertical angles D) 1 and 4 are alternate int. angles

4) Refer to the diagram.

A) Name a pair of same-side interior angles.

B) Name a pair of corresponding angles.

C) Name a pair of alternate interior angles.


5) find the coordinates of the vertices of the image ABCD for each transformation.

A) Translation (x, y) (x + 4, y – 2) B) reflection across x = -1 C) rotation of 180o about the origin D) Dilation with scale factor of 2 about the origin

6) How many lines of symmetry does a square have?

7) Classify the triangle by its sides.

8) Classify the triangle by its angles.

9) Find the value of x.

10) Find the value of x if AC = 20.


11) Find the value of x if B is the midpoint of .

12) a. Find TQMm . b. Find the value of x.

13) MK is the bisector of AB. Find the value of each variable. (not drawn to scale)


15) Find the measure of the sides of equilateral JKL if JK = 5x – 7 and JL = 2x + 5.

16) ⃗⃗ ⃗⃗ ⃗ bisects PQR. If m 1 = 4x -12 and m 2 = 2x + 6, find m XQR.



18) What is the intersection of planes ADFE and EFCB?

19) What is the intersection of planes AXYC and BWYC?

20) What is the intersection of planes ABFE and BCGF?

21) Find the intersection of MN and LO .

22) Use the diagram to…

a) Name ABC in 2 other ways

b) Name ⃡⃗⃗⃗ ⃗ in another way.

c) Give all other names for ⃗⃗⃗⃗ ⃗ in all other ways.

d) Name a pair of complementary angles.


23) Find the slope of a line perpendicular to 3y + 2x = 4.

24) What is the slope of the line that contains (6, -4) and (-4, 1)?

25) Which pair of lines is perpendicular?

A) y = 3x + 5 B) y = 4x - 5

y = -3x – 8 y = 4x + 2

C) y = 5x – 3 D) y =

y =

x + 3 y =

x – 5

26) Which pair of lines is parallel?

A) y-13 = 5(x-2) B) y+3 = -2(x – 1 )

5x + y = 10 2x + y = 4

C) y = 3x + 8 D) x = 3

3x + y = 6 y = 3

27) Graph a line parallel to y = 3x – 1 that contains (2, 3).

28) Graph a line perpendicular to y =

x – 5 that contains (-2, 2).

Equations of Lines

Slope-intercept form y = mx + b where m is

the slope and b is the y-intercept

Point-slope form y – y1 = m(x – x1) where m is

the slope and the point on the line is (x1, y1)


3 ft

9 ft

11 ft

5 ft

29) What is the distance between (-1, 6) and (5, -2)?

30) The two rectangles are similar. Which is a correct proportion for corresponding sides?

a.

b.

c.

d.

31) The skyscraper in Chicago is 1450 feet high. A model of the skyscraper is 24 inches tall. What is the ratio of

the height of the model to the height of the actual skyscraper?

32) Solve the proportion.

33) The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the

second. The figures are not drawn to scale.

34) Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.

x

8 m

4 m

12 m

15 18


35) You want to produce a scale drawing of your living room, which is 24 ft by 15 ft. If you use a scale of 4 in. = 6

ft, what will be the dimensions of your scale drawing?

36) Figure . Name a pair of corresponding sides?

37) ABCD ~ WXYZ. AD = 6, DC = 3, and WZ = 59. Find ZY. The figures are not drawn to scale.

38) Triangles ABC and DEF are similar. Find the lengths of AB and EF.

State whether the triangles are similar. If so, write a similarity statement, the similarity ratio and the postulate

or theorem you used.

39) a. b. In ABC, AB = 8, AC = 10 and A = 24o. In

DEF, DE = 12, DF = 15 and D = 24o.

A

B C

D

FE

4

55x

x


40) Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the

diagram. What is the distance between the two campsites? The diagram is not to scale.

41) Use the Side-Splitter Theorem to find x, given that .

42) Find the length of the missing side. The triangle is not drawn to scale.

43) Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.

B

A

C

P Q

8

x 18

12

25

24

45°

16

Not drawn to scale

25

24


44) Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

Not drawn to scale

45) Write the tangent ratios for and .

46) A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole

casts a 249-foot-long shadow. Find the angle of elevation to the nearest degree.

47) Find the value of x. Round to the nearest tenth.

30°

x y

20

R Q

P

21

20

29

Not drawn to scale

10

x

Not drawn to scale


48) A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an

entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight

to the entrance door?

49) State the postulate or theorem you can use to prove the triangles congruent. If the triangles cannot be

proven congruent, write not possible.

50) If then which of the following are not true?

A) MRELDQ B) EMRDLQ C) QLDRME D) LQDMRE

51) . What angle is congruent to ?Y

52) Name a pair of overlapping congruent triangles. State whether the triangles are congruent by SSS, SAS, ASA,

AAS, or HL.


53) Which two sides must be congruent to use ASA to prove JCXDMX ?

54) Which two angles must be congruent to use SAS to prove CBXADX ?

55) Are the triangles congruent? If so, write a congruence statement and justify your reasoning. If not, write not

congruent.

56) Given: ||

||

Prove:

57 ) Given: and bisect each other at G.

Prove: E I


58) Given: JKMJ

MLKL

MLJK

Prove: KLJM

59) Given: AED is isosceles

CDAB

Prove: BEC is isosceles

60) Conditional: If it is raining, then the ground is wet.

a) Write the converse of the statement. _______________________________________________________

61) Is the following statement a good definition?

A square has four right angles.

62) Find a counterexample for the statement. If shapes are similar, then they are congruent.

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Semester 1 Exam Review Name: Geometry Geometry Sem 1 Final ...rohls.weebly.com/uploads/2/8/2/1/2821453/geo_sem_1_final_exam... · Semester 1 Exam Review Name: _____ Geometry 11) Find