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Geometry Semester 1 Name: _____________________________ Final Exam Review 2018 - 19 Date: __________ Period: __________

Formulas: Definitions:

1. Slope - 1. Complementary –

2. Midpoint - 2. Supplementary –

3. Bisect –

3. Distance - 4. Vertical Angles –

4. Pythagorean Theorem – 5. Perpendicular –

5. Point – slope Form –

6. Slope – Intercept Form – Triangle Congruence Criterion:

Transformations:

1. Translation – Triangle Similarity Criterion:

2. Reflections –

3. Rotations – Type of Sentences:

a. 𝑅 , ° 1. Conditional –

b. 𝑅 , ° a. Hypothesis –

c. 𝑅 , ° b. Conclusion –

4. Rotational Symmetry – 2. Converse – 3. Inverse –

4. Contrapositive –

5. Conjecture –

6. Bi – Conditional –

Theorems: All radii of a circle are congruent If two lines are parallel, then their slopes are equal If two lines are perpendicular each line’s slope is the opposite reciprocal of the other’s The sum of the measures of the angles in a triangle is 180 degrees The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote

interior angles A segment joining the midpoints of two sides a of a triangle is parallel to the 3rd side, and its

length is one half the length of the 3rd side (Triangle Midsegment Theorem) The median of a trapezoid is parallel to the bases and its length is the average of the lengths of the

base. (Trapezoid Median Theorem)

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Properties and Definitions

Quadrilaterals:

Parallelogram: Kite:

1. 1.

2. 2.

3. 3.

4. 4.

5. 5. Rectangle: Trapezoid:

1.

2.

Plus all 5 properties of the Parallelogram Isosceles Trapezoid:

Rhombus: 1.

1. 2.

2.

3.

Plus all 5 properties of the Parallelogram Square: Ways to prove Quad. is a parallelogram

All 5 properties of the Parallelogram 1.

2 properties of the Rectangle 2.

3 properties of the Rhombus 3.

4.

5.

3

Q

P

R

U

T

S

Geometry Semester 1 Name: _____________________________ Final Exam Review 2018 – 2019 Date: ____________ Period: __________ UNIT 1 – ACTIVITIES 1 – 8 1. Identify the following on the given picture:

a. Chord:

b. Diameter:

c. Radius:

d. Center:

2. Given Circle P. a. Put the following segments in order from smallest to largest: 𝐴𝐵, 𝐷𝐵, 𝑃𝐶 b. If AC = 12, find PD.

3. Write all possible names for ∠2?

__________ 4. Suppose point D is in the interior ∠𝐴𝐵𝐶, 𝑚∠𝐴𝐵𝐶 = 12𝑥 − 110, 𝑚∠𝐴𝐵𝐷 = 3𝑥 + 40, and 𝑚∠𝐷𝐵𝐶 = 2𝑥 − 10. What is 𝑚∠𝐴𝐵𝐶?

5. Which angle pairs in the figure are adjacent and supplementary? Check all that apply.

_______ ∠𝐷𝐵𝐶 and ∠𝐶𝐵𝐸

_______ ∠𝐴𝐵𝐷 and ∠𝐶𝐵𝐸

_______ ∠𝐴𝐵𝐹 and ∠𝐹𝐵𝐸

_______ ∠𝐴𝐵𝐷 and ∠𝐷𝐵𝐶

_______ ∠𝐶𝐵𝐸 and ∠𝐸𝐵𝐴

A

D

B C

F E

AB

C

D

2 1

A

D P

B

C

4

__________ 6. In the diagram shown, AB ⊥ PQ. If PT = TQ, which statement is true?

A. AT = TB B. 𝑃𝑄 is the perpendicular bisector of 𝐴𝐵

C. 𝐴𝐵 is the perpendicular bisector of 𝑃𝑄 D. 𝑃𝑇 is the perpendicular bisector of 𝐴𝐵

__________ 7. Find the measure of 1m .

__________ 8. Alison states ∠𝐴𝑀𝐶 + ∠𝐶𝑀𝐷 + ∠𝐷𝑀𝐵 = ∠𝐴𝑀𝐵. Which justifies Alison’s statement?

A. Angle Addition Postulate B. Segment Addition Postulate C. Construction of an Angle Bisector D. Construction of a Perpendicular Bisector

__________ 9. Suppose 𝑄 is the midpoint of 𝑃𝑅, 𝑃𝑄 = 𝑥 + 10, and 𝑄𝑅 = 4𝑥 − 2. What is the value of 𝑃𝑅

__________ 10. If ∠𝐷 and ∠𝐶 are complementary, 𝑚∠𝐶 = 3x and 𝑚∠𝐷 = 4x + 6, find 𝑚∠𝐶.

__________ 11. For 𝐴𝐵, point A has coordinates (3, -5) and point B has coordinates (-1, 9). What are the

coordinates of the midpoint of 𝐴𝐵?

__________ 12. Julie is given two points, A(5, 4) and B(3, -2). Find AB.

P

Q

T

B

A

1 ° °

5

p

n

m

8 7 6 5

4 3 2 1

__________ 13. Name each angle pair in the given diagram.

A. ∠2 and ∠6 B. ∠8 and ∠5 C. ∠4 and ∠5 D. ∠4 and ∠6

__________ 14. Billy is working on a proof given 𝑥 ∥ 𝑡 and 𝑘 ∥ 𝑤 as shown. He wants to write a statement that

can be justified using only the Corresponding Angles Postulate. Which statement could he write?

A. ∠2 and ∠4 B. ∠2 and ∠6 C. ∠2 and ∠8 D. ∠2 and ∠10

__________ 15. Use the diagram from #14. Given 𝑥 ∥ 𝑡 and 𝑘 ∥ 𝑤 if 𝑚∠12 = 110°, find 𝑚∠3.

__________ 16. How could you justify that Δ𝐴𝐵𝐶 is a right triangle?

A. The slope of 𝐵𝐶 = − and the slope of 𝐵𝐴 = −

B. The slope of 𝐶𝐴 = and the slope of 𝐵𝐴 = −

C. The slope of 𝐵𝐶 = − and the slope of 𝐶𝐴 =

D. The slope of 𝐵𝐶 = − and the slope of 𝐵𝐴 = −

A( 3, 1 )

B( -6, 4 )

C( -3, -2 )

16

9 10 11

12

13 14 15

7 6 5

4 3 2 1

t x

k

w 8

6

17. What is the equation of the line parallel to the line 5𝑦 + 2𝑥 = −25 and passes through the point (5, −3). 18. Write the equation of the line that is parallel to the line 𝑦 = −2𝑥 + 3 and passes through the point ( -7, 9 ). 19. Write the equation of the line perpendicular to the line 𝑥 + 𝑦 = 2 and passes through the point ( -5, 8 ).

20. What is the equation that represents a line perpendicular to the line shown on the graph through the same y-intercept?

21. Circle the hypothesis of the conditional statement below and underline the conclusion.

Conditional: If it is snowing, then we will make a snowman.

( -3, 3 )

( 3, -1 )

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__________ 22. Consider the conditional statement shown.

If a student plays the trumpet, then the student is in the school band.

Which is a counterexample to this conditional statement?

A. A student can be in the band but not play the trumpet B. A student may not be in the band and not play the trumpet C. A student can play the trumpet but not be in the school band D. A student may not play the trumpet but still be in the school band

__________ 23. The distance between two points on a number line is 8 units. Point A is at 6. What are possible location(s) for point B.

UNIT 2 – ACTIVITIES 9 – 16 24. Consider the arrows on the coordinate grid. Name a transformation that shows the figures are congruent.

25. Complete the table using the translation of a rectangle (x, y) → (x - 1, y + 3).

Point Preimage Image A (2,-1)

B (2, -3)

C (6,-1)

D (6,-3)

26. Regular polygons have rotational symmetry with angles of rotation listed below. Name each polygon. a. 36°

b. 60°

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27. Complete the table below by listing the image vertices after a transformation 𝑟 .

28. The band is practicing a new rigid transformation halftime routine. What happens to the distance between

each band member as they move?

29. Describe each mapping as a single transformation:

a. Figure 1 Figure 3 b. Δ𝑂𝑀𝑁 Δ𝐵𝐴𝐶

30. Describe the translation using coordinate notation. 31. Suppose Δ𝑄𝑅𝑆 and Δ𝑇𝑈𝑉 are congruent right triangles such that ∠𝑅 is a right angle and ∠𝑉 = 35° 𝑎𝑛𝑑 ∠𝑇 = 5𝑥. Solve for x.

Point Preimage Image A (2,-1)

B (2, -3)

C (6,-1)

D (6,-3)

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32. Given the information provided, name the method, if any, that can be used to prove the triangles congruent:

33. What additional information need to be given to develop the proof that LHJFHN by ASA congruence criteria?

34. What additional information need to be given to develop the proof that CDBABD by SAS congruence criteria?

35. What additional information need to be given to develop the proof that EMREMH by HL congruence criteria?

36. Which statement could be used in a proof with the reason CPCTC after proving Δ𝐴𝐵𝐶 ≅ Δ𝐸𝐹𝐺? Circle all that apply.

A. 𝐴𝐶 ≅ 𝐸𝐺

B. 𝐴𝐵 ∥ 𝐸𝐹

C. 𝐵𝐶 ≅ 𝐹𝐺

D. ∠𝐵𝐶𝐴 ≅ ∠𝐹𝐺𝐸

E. ∠𝐶𝐵𝐴 ≅ ∠𝐺𝐸𝐹

37. What are the ways to prove two triangles are congruent?

H J F

N L

A

D

C

B

E

M R H

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__________38. Given two triangles with the properties shown.

What additional information needs to be marked to develop the proof that Δ𝐴𝐵𝐶 ≅ Δ𝐴𝐷𝐶 by the ASA congruence criteria?

A. ∠1 ≅ ∠2 and ∠𝐵 ≅ ∠𝐷

B. 𝐴𝐵 ≅ 𝐵𝐶 and 𝐴𝐷 ≅ 𝐶𝐷

C. ∠1 ≅ ∠2 and ∠𝐵𝐴𝐶 ≅ ∠𝐷𝐴𝐶

D. 𝐶𝐷 ≅ 𝐵𝐶 and 𝐴𝐵 ≅ 𝐴𝐷

__________39. RST has angle measures given by 299 xRm , xSm 593 , and 210 xTm . What is the measure of T ?

__________40. Find m∠𝑉.

41. Write a two-column proof.

A

D

C

B

2 1

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Congruence is reflexive

42. Using the flowchart proof, FILL IN THE BLANKS on the corresponding two-column proof.

Given: Isosceles Δ𝐹𝐺𝐻 with base 𝐺𝐻 and median 𝐸𝐹. Prove: Δ𝐺𝐹𝐸 ≅ Δ𝐻𝐹𝐸

Statement Reasons

1. Isosceles FGH with base GH 1. Given

2. 2. Definition of isosceles triangle

3. EF is a median 3. Given

4. 4. Definition of median

5. EFEF 5.

6. HFEGFE 6. SSS Congruence Postulate

43.

44. When can you use CPCTC?

F

G E

H

SSS Congruence Postulate

Definition of median

Definition of Isosceles triangle

Isosceles Δ𝐹𝐺𝐻 with base 𝐺𝐻

Given

𝐺𝐹 ≅ 𝐻𝐹

Δ𝐺𝐹𝐸 ≅ Δ𝐻𝐹𝐸 𝐸𝐹 is a median 𝐺𝐸 ≅ 𝐻𝐸

Given

EF ≅ EF

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__________ 45. What values of x and y would prove that PQ is the midsegment of trapezoid JKLM.

__________ 46. Which of the following are sufficient to prove a quadrilateral is a parallelogram?

I. Show both pairs of opposite sides parallel. II. Show both pairs of opposite angles are congruent. III. Show both pairs of opposite sides congruent. IV. Show one pair of opposite sides are both parallel and congruent. V. Show the diagonals bisect each other.

A. I, II, III only B. I, II, III, and IV only C. I, II, III, and V only D. I, II, III, IV and V

__________ 47. Which statement cannot be used to show that quadrilateral XYZW is a parallelogram?

A. 𝑋𝑌 ∥ 𝑊𝑍 and 𝑌𝑍 ∥ 𝑋𝑊 B. XW = WZ and XY = YZ C. ∠𝑊𝑋𝑌 ≅ ∠𝑌𝑍𝑊 and ∠𝑋𝑌𝑍 ≅ ∠𝑍𝑊𝑋 D. 𝑋𝑌 ≅ 𝑊𝑍 and 𝑋𝑊 ≅ 𝑌𝑍

__________ 48. Given the diagram in #48 is a parallelogram, if 𝑚∠𝑊 = 72°, find the other 3 angle measures.

__________ 49. Which of the following must be a parallelogram? Select all that apply.

a. b. c. d.

__________ 50. Given square QRST, solve for x and y.

J

L

Q

K

x

P 4 y

M

10

X Y

Z W

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UNIT 3 – ACTIVITIES 17 – 18

51. The original photo of the basketball team is 4 inches by 6 inches. The school wants to enlarge it to display it in the gym. If the enlargement has a new width of 5 feet, then find the new length.

For questions 53 and 54, use the following diagram.

52. Classify the dilation from Δ𝐴𝐵𝐶 → Δ𝐴’𝐵’𝐶’. 53. State the scale factor from Δ𝐴𝐵𝐶 → Δ𝐴’𝐵’𝐶’.

__________ 54. Ramon places a mirror on the ground 45 ft from the base of a flagpole. He walks backwards until he can see the top of the flagpole in the middle of the mirror. At that point, Ramon’s eyes are 6 ft above the ground and he is 7.5 ft from the mirror. What is the height of the flagpole.

55. Given that the triangles are similar, solve for x.

E

D

C

A

B

A’

B’ C’

6

8

5

B C

36

48

30

A