First Semester Final Exam Review Name___________________________

Geometry

→From Standard A…

1) If BO ⊥ OD, find each of the following:

a) X = ________

b) mAOB = _____

c) mCOD = _____

d) mAOD = _____

2) Find x in each diagram.

4) If A and B are complementary angles, A = 7x – 9 and B = 2x, find mA.

5) A is the midpoint of 𝐶𝐷̅̅ ̅̅ . Find length of 𝐴𝐶̅̅ ̅̅ if CD = 8x + 2 and AD = x + 25.

6) 1 and 2 are a linear pair. m1 = x – 39 and m2 = x + 61. What is the measure of the obtuse angle in the

pair?

7) 1 and 2 are supplementary, and 2 and 3 are complementary. If 1 = 149, find m3.

24 2x - 12

8) X and Y are vertical angles. Y and Z are complementary. If mZ is 57o, what is the measure of X?

9) Name…

a) Two angles that form a linear pair with ∠𝐸𝐾𝐻.

b) An angle that is vertical to ∠𝐹𝐾𝐺

c) Two angles that are complementary with ∠𝐺𝐾𝐽

(**hint: look at your answer for (b))

d) An angle supplementary with ∠𝐺𝐾𝐽

10) MC. Find the length of the segment below. 11) If k ⊥ t, circle all statements that are true.

12) Find the midpoint and length of C(-2, 3) and D(2, -1). Sketch a graph and check that your answers make sense.

13) (HONORS) Find the indicated length.

a. b.

→From Standard B…

14) Fill in the blank with sometimes always or never. Explain your answer. “If two angles are congruent, then they

are _________________ adjacent.”

Xo Zo

Wo

a) x = z + w

b) y > z + w

c) y > x + w

d) y + z + w =180

e) x + w + y = 180

f) y + w = 90

g) w + y > x

Yo

k

t

15) Find the next number in the pattern.

a) 1, 1

3 ,

1

9 ,

1

27 , … b) 3, -6, 12, -24, … c) 5, 10, 15, 20, 25, … d) 6, 9, 15, 24, 36,…

16) Draw a diagram and write a conjecture that is ALWAYS TRUE and a conjecture that is only SOMETIMES TRUE.

a) 𝐵𝐶⃗⃗⃗⃗ ⃗ is in the interior of DBF b) 1 and 2 form a linear pair

17) Find a counterexample for the following conjecture based on the given statement.

Given: P is between 𝐴𝐵̅̅ ̅̅ Given: 1 and 2 are complementary

Conjecture: 𝐴𝑃̅̅ ̅̅ ≅ 𝑃𝐵̅̅ ̅̅ Conjecture: 1 and 2 are 45 degrees

18) Cross off the statement(s) you canNOT assume from the diagram.

→From Standard C…

19)

A,B,C are collinear Line AC and Ray DB intersect at B

AB = BC ∠𝐷𝐵𝐸 𝑎𝑛𝑑 ∠𝐸𝐵𝐶 are adjacent angle

Angle DBE is congruent to EBC 𝑚∠𝐷𝐵𝐸 + 𝑚∠𝐸𝐵𝐶 = 90

𝑚∠𝐴𝐵𝐶 = 180 Ray DB is perpendicular to line AC

Ray BE bisects DBC AB + BC = AC

𝑚∠𝐷𝐵𝐶 + 𝑚∠𝐷𝐵𝐴 = 180 𝑚∠𝐷𝐵𝐸 + 𝑚∠𝐸𝐵𝐶 = 𝑚∠𝐷𝐵𝐶

20) Determine the angle relationship: linear pair, vertical angles, corresponding, alt interior, alt exterior, or

consecutive interior.

a) 11 and 7

b) 9 and 13

c) 4 and 5

d) 12 and 10

e) 6 and 3

21) Determine which statements below would allow you to conclude that a || m. Justify your reasoning

with a postulate or theorem.

a. m<4 = m<5

b. m<3 + m<5 = 180

c. m<5 + m<6 = 180

22)

23) What is the slope of a line that…

a. is parallel to 2y = x + 1 b. perpendicular to y = 3x -7 c. perpendicular to 2𝑦 + 3𝑥 = 5

24) Write the equation of a line in slope intercept form that contains each pair of points. You graph paper if you

need!

a. (−1, 6) 𝑎𝑛𝑑 (5, −6) b. (3, 4) 𝑎𝑛𝑑 (10,−3)

d. m<8 = m<1

e. m<8 = m<5

f. m<6 = m<4

25) Write the equation of a line in slope intercept form that…(use graph paper if you need!)

a. Is perpendicular to 𝑦 = 4𝑥 − 1, and contains (4,3) b. Is parallel to 𝑦 = −2

3𝑥 and contains (6, -5)

c. Is parallel to 𝑦 = 2𝑥 + 1 and passes through (2,5) d. is perpendicular to y = 4x + 1 and passes through (8,1)

26) To prove p|| q…

a. We would need m< 3 + _______ = 180

b. We would need m<1 = _____, or m<1 = _______

c. We would need <8 and <7 to be _____________.

d. We would need m<9 = m< ________, or m<9 = ________.

27) (HONORS) Which lines (if any!) are

parallel in the diagram?

Be sure to justify your answer

mathematically and with an explanation!

→From Standard D…

28) Find the value of the missing variables.

29)

30) For EGF 𝑚∠𝐸 = 𝑚∠𝐺. Find the perimeter of the triangle if EF = 4x, EG = 14, and FG = 2x + 6.

31)

32) COMPLETE THE PROOF BELOW.

Given: ABCD is a parallelogram

Prove: 𝐴𝐵 ≅ 𝐶𝐷

Statements Reasons

1. 1. Given

2. AB || CD 2. Def. of _______________

3. ∠BAC ≅ ∠𝐴𝐶𝐷 3.

4. 4.

5. 5. Reflexive

6. ⊿𝐵𝐴𝐶 ≅ ⊿𝐷𝐶𝐴 6.

7. 𝐴𝐵 ≅ 𝐶𝐷 7.

The City of Whoville is shown below. City Hall is located at (-4,3), the local primary school is located at (5,2), and the

beloved Library is located at (8,-4). Use the layout of the Wonderful City of Whoville to answer the questions below.

1. The Grinch’s home is located exactly in the middle of the School

and the library. What are the coordinates of his location?

2. The Grinch’s dog, Max, is 2 blocks WEST and 1 block south from

the library. What is his location?

3. Write the equation of the line (in slope-intercept form) that

connects Max’s location and the Library’s location.

Use the picture below to write two FLOW CHART PROOFs

4. Prove x || y,

given that ∠1 and ∠6 are supplementary

5. Prove x || y,

given that ∠8 and ∠5 are supplementary

6. (HONORS) Write a FLOW CHART PROOF

7. (HONORS) Write a FLOW CHART PROOF

8. Write a TWO COLUMN proof.