Geometry - Dearborn Public Schools



Final Exam Review

Geometry Semester 1 Name:______________________

Vocabulary and Notation- Final Review part 1

|Vocabulary: |Notation/Rule |Picture |

|Point | | |

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|Line | | |

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|Plane | | |

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|Ray | | |

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|Segment | | |

|Collinear points | | |

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|Coplanar points | | |

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|Congruent | | |

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|Supplementary angles | | |

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|Linear pair | | |

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|Complementary angles | | |

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|Vertical angles | | |

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|Corresponding angles | | |

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|Alternate interior angles | | |

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|Alternate exterior angles | | |

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|Consecutive interior angles | | |

|Reflection | | |

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|Rotation | | |

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|Translation | | |

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|Dilation | | |

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|Rigid | | |

|Transformations | | |

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|Vertical stretch | | |

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|Horizontal Stretch | | |

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|Angle Bisector | | |

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|Altitude | | |

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|Midpoint | | |

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|Median | | |

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2. Lines, Segments, Rays, Angles, plans

|a) Name the line four different ways. |b) Draw [pic] |c) Draw [pic] |

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|d) Draw [pic] with a protractor such that [pic] |e) Draw three collinear points A, B, and C. |f) Name the plane two different ways. |

|a) Name plane that represents the top of the box. |d) Name the intersection plane VUY , plane TUX, and | |

| |plane SVT. | |

|b) Name the intersection plane SVW and plane STX. | | |

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|c) Name another point on plane SWX. |e) Name the planes whose intersection is [pic]. | |

|Use the figure on the right to… |d) Name a supplement of (DOE. | |

|a) Name a right angle. | | |

| |e) Name two angles that are complementary. | |

|b) Name an acute angle. | | |

| |f) Name two segments that are perpendicular. | |

|c) Name an obtuse angle. | | |

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3. Circle the statements that are true and use correct notation for each diagram. Cross out the incorrect statements. Make sure you understand the difference between = & (, [pic]& [pic], and [pic] & [pic].

|a) |b) |

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|[pic], [pic], [pic], | |

| |[pic] [pic] [pic] [pic] |

|[pic]cm, [pic]cm | |

| |[pic] [pic] [pic] |

4. Use the set of parallel lines cut by a transversal below to answer the questions bellow.

a. In the figure above, what set of angles are vertical?

|A. |[pic] & [pic] |C. |[pic] & [pic] |

|B. |[pic] & [pic] |D. |[pic] & [pic] |

b. In the figure above, what set of angles are supplementary?

|A. |[pic] & [pic], they are same-side interior angles |C. |[pic] & [pic], they are alternate interior angles |

|B. |[pic] & [pic], they are vertical angles |D. |[pic] & [pic], they are corresponding angles |

c.. In the figure above, what set of angles are corresponding angles?

|A. |[pic] & [pic], they are congruent |C. |[pic] & [pic], they are supplementary |

|B. |[pic] & [pic], they are congruent |D. |[pic] & [pic], they are supplementary |

d. In the figure above, what set of angles are alternate interior angles?

|A. |[pic] & [pic], they are a linear pair |C. |[pic] & [pic], they are congruent |

|B. |[pic] & [pic], they are congruent |D. |[pic] & [pic], they are a linear pair |

___ 5. If BCDE is congruent to OPQR, then [pic] is congruent to [pic]

|a. |[pic] |b. |[pic] |c. |[pic] |d. |[pic] |

___

5. [pic]

[pic]

6. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

7- List all rigid transformations and explain why they are called rigid. Give an example

8- List all the non-rigid transformations and explain why they are called rigid. Give an example

9- Name each type of transformation (choices: reflection, rotation, translation)

a.

10. Which one of the below transformation preserve congruence? Select all that apply

[A] translation [B] reflection

[C] rotation [D] dilation

Final Exam Review

Geometry Semester 1 Name:_______________________

Applying Transformations- Final review part 2

|1. Transform the triangle from |2. If triangle ABC is rotated 180° about the origin which of the following are the |

|(x,y) to (x + 7, y) |coordinates of [pic]. |

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| |A (4,–3) B (–4,–3) C (–3,–4) D (3,–4) |

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|3. Reflect the triangle across the x-axis. |4. Describe in words the result of applying each rule. |

|Write the rule: (x,y) to ( , ) |(x,y) to [pic] |

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| |(x,y) to [pic] |

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| |(x,y) to [pic] |

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| |5. Write the rule for each description. |

| |translate 4 units up |

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| |reflect over y-axis |

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| |translate 2 units left |

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|6. The vertices of (ABC are A(3, –1) , B(3, 4), and C(0, 1). If (ABC is |7. Which expression describes the translation of a point from (5, –2) to (8,–6)? |

|translated 2 units down and 3 units to the right to create (DEF, what are the | |

|coordinates of the vertices of (DEF. |A 3 units left and 4 units up |

|A D(6,–3) E(6, 2) F(3,–1) |B 3 units right and 4 units up |

|B D(1,2) E(1, 7) F(–2,4) |C 3 units left and 4 units down |

|C D(6,–4) E(6, 1) F(3,0) |D 3 units right and 4 units down |

|D D(5,–3) E(5, 2) F(2,–1) | |

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8. Which graph shows a triangle and its reflection image in the y-axis?

[A] [pic] [B] [pic]

[C] [pic] [D] [pic]

9. Which graph shows a triangle and its rotation image about the origin?

[A] [pic] [B] [pic]

[C] [pic] [D] [pic]

10. Which graph shows a triangle and its reflection image in the x-axis?

[A] [pic] [B] [pic]

[C] [pic] [D] [pic]

11. Show the image of the vertex marked A, in the triangle below after a

rotation of 180 degrees about the origin.

[pic]

[A] ( -4, 6 ) [B] ( 4, -6 ) [C] ( 6, 4 ) [D] ( 4, 6 )

12. Point A (1, 4) is reflected over the y-axis. Write the coordinates of A′.

[A] (–1, 4) [B] (–1, –4) [C] (1, –4) [D] (1, 4)

13. Point A (6, –3) is reflected over the x-axis. Write the coordinates of A′.

[A] (–6, –3) [B] (6, –3) [C] (6, 3) [D] (–6, 3)

14. Write a rule to describe the translation of ΔABC to ΔA′B′C′.

[pic]

[A] four units left and three units down

[B] four units left and five units down

[C] five units right and four units up

[D] four units right and three units up

15. The dotted triangle is a dilation image of the solid triangle. What is the scale factor?

[pic]

[A] 2 [B] 3 [C] [pic] [D] [pic]

16. Draw the image of the following triangle when it is dilated about the origin by a factor of 2. What are the coordinates of the vertices of the image?

[pic]

[A] (2, 2) (6, 0) (8, 8) [B] (2, 2) (6, 6) (8, 6)

[C] (2, 2) (6, 0) (8, 6) [D] (2, 2) (6, 6) (8, 8)

Final Exam Review

Geometry Semester 1 Name:__________________

Prove and justify- Final Review part 3

1- What else must you know to prove the triangles congruent by ASA? By SAS?

[pic]

|a. |[pic]; [pic] |c. |[pic]; [pic] |

|b. |[pic]; [pic] |d. |[pic]; [pic] |

2- Name the theorem or postulate that lets you immediately conclude [pic]

[pic]

|a. |SAS |b. |ASA |c. |AAS |d. |none of these |

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3- Supply the missing reasons to complete the proof.

Given: [pic] and [pic]

Prove: [pic]

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|a. |ASA; Substitution |c. |AAS; CPCTC |

|b. |SAS; CPCTC |d. |ASA; CPCTC |

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4. Supply the reasons missing from the proof shown below.

Given: [pic], [pic]

Prove: [pic]

[pic]

|a. |ASA; CPCTC |c. |SSS; Reflexive Property |

|b. |SAS; Reflexive Property |d. |SAS; CPCTC |

Use the figure below to answer the next 3 questions.

[pic]

____ 5. Which statement proves lines m and n are parallel?

|A. |[pic] & [pic] are alternate exterior angles and |C. |[pic] & [pic] are same-side exterior angles and |

| |supplementary | |supplementary |

|B. |[pic] & [pic] are alternate exterior angles and |D. |[pic] & [pic] are same-side exterior angles and |

| |congruent | |supplementary |

6. Which statement proves lines m and n are parallel?

|A. |[pic] & [pic] are alternate exterior angles and |C. |[pic] & [pic] are same-side exterior angles and |

| |congruent | |supplementary |

|B. |[pic] & [pic] are alternate exterior angles and |D. |[pic] & [pic] are alternate interior angles and |

| |supplementary | |supplementary |

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7. Which statement proves lines m and n are parallel?

|A. |[pic] & [pic] are alternate interior angles and |C. |[pic] & [pic] are same-side interior angles and |

| |supplementary | |supplementary |

|B. |[pic] & [pic] are alternate interior angles and |D. |[pic] & [pic] are alternate interior angles and |

| |congruent | |congruent |

____ 8. Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement?

[pic]

|a. |Yes; [pic]. |

|b. |Yes; [pic]. |

|c. |Yes; [pic]. |

|d. |No, the triangles cannot be proven congruent. |

9. Based on the given information, can you conclude that [pic]? Explain.

Given: [pic], [pic], and [pic]

10. Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to prove that[pic].

[pic]

11. Is [pic] by HL? If so, name the legs that allow the use of HL.

[pic]

12. Separate and redraw [pic] and [pic]. Identify any common angles or sides.

[pic]

13. Write a two column proof to show that [pic].

Given: [pic] and [pic]

[pic]

14. Complete the below proof

[pic]

Given m//n

Prove that ................
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