Download geom exam review chapters 1_2_3_4_7

Geometry 1st Semester Exam REVIEW
Chapters 1-4, 7
Chapter 1 Basics of Geometry:
1. (a) What does the symbol ̅̅̅̅
𝐴𝐵 represent?
⃗⃗⃗⃗⃗ represent?
(b) What does the symbol 𝐴𝐵
(c) What does the symbol ⃡⃗⃗⃗⃗
𝐴𝐵 represent?
2. Classify the following angles:
(a) 25
(b) 90
(c) 178
(d) 180
(e) 39
3. Find the midpoint of a segment with endpoints:
(a) (-9, 1) and (5, -3)
(b) (12, -8) and ( -4, 10)
4. ⃗⃗⃗⃗⃗⃗
𝐵𝐷 bisects ABC. mABD is shown to be 65. What is the measure of ABC?
5. Find the area of a:
(a) triangle with a base of 5 cm and a height of 12 cm.
(b) rectangle with a length of 14 in and a width of 20 in.
(c) circle with a radius of 5 m.
6. Find the area of the figure. Use 3.14 for 𝜋 in part (a).
(a)
(b)
7. The measure of A is 76.
(a) Find mB if A and B are complementary.
(b) Find the mC if A and C are supplementary.
8. Use the following diagram:
(a) If m2 = 120, then m4 = ?
(b) If m1 = 50, then m4 = ?
(c) If m3 = 133, then m1 = ?
(d) If m 1 = 104, then m2 = ?
9. Find the circumference of a circle with a: (use 3.14 for 𝜋).
(a) radius of 13 in.
(b) diameter of 12 in.
10. B is between points A and C. Find the value of x and the length of BC if
AB = 3, BC = 4x+1, and AC = 8.
11. Use the following diagram:
(a) Name a point that lies on line s.
(b) Name all points that are collinear to
points B and D.
s
(c) Name a point that is coplanar to line s.
12. Find the distance between points C(6, 3) and D(4, 7).
13. What is m1 if m2 = 115?
14. Find the area and perimeter of the rectangle shown.
Chapter 2 Logic and Reasoning:
15. Write the following sentence in if-then form.
“An angle is acute if its measure is less than 90.”
̅̅̅̅̅̅ ≅ 𝑋𝑌.
̅̅̅̅̅ What is the value of x?
16. In WXYZ, 𝑊𝑍
W
X
3x + 9
8x - 11
Z
Y
17. State the property that supports the statement.
(a) AB = AB
(b) If AB = YZ, then YZ = AB
̅̅̅̅̅, 𝑎𝑛𝑑 𝑊𝑋
̅̅̅̅̅ ≅ ̅̅̅̅
(c) If ̅̅̅̅
𝑅𝑆 ≅ 𝑊𝑋
𝑌𝑍, 𝑡ℎ𝑒𝑛 ̅̅̅̅
𝑅𝑆 ≅ ̅̅̅̅
𝑌𝑍.
18. Fill in the missing reasons on the proof shown about segment length.
Given: AM = MB
Prove: ½ AB = MB
Statements
AM = MB
Reasons
Given
AB = AM + MB
?
AB = MB + MB
?
AB = 2MB
?
½ AB = MB
?
⃡⃗⃗⃗ ⊥ ⃗⃗⃗⃗⃗
⃡⃗⃗⃗⃗ ⊥ 𝐻𝐷
⃡⃗⃗⃗⃗ , find the angle measures.
19. Given that 𝐶𝐺
𝐴𝐸 𝑎𝑛𝑑 𝐵𝐹
(a) If m3 = 28, then m5 = ?
(b) If m5 = 39, then m4 = ?
(c) If mCAF = 142, then mGAB = ?
Chapter 3 Parallel & Perpendicular Lines:
20. Find m1 if m2 = 28.
1
2
21. Write an equation of a line with a y-intercept of 10 and is:
3
(a) parallel to the line 𝑦 = − 4 𝑥 + 9
3
(b) perpendicular to the line 𝑦 = − 4 𝑥 + 9
22. Given the following equations:
3
A. 𝑦 = − 4 𝑥 + 9
(a) Identify which two lines are parallel.
4
B. 𝑦 = − 3 𝑥 − 5
3
C. 𝑦 = − 4 𝑥 + 1
(b) Identify which two lines are perpendicular.
4
D. 𝑦 = 3 𝑥 − 6
3
E. 𝑦 = 4 𝑥 − 2
23. Use the following diagram to identify angle relationships.
(a) Identify a pair of corresponding angles.
(b) Identify a pair of alternate exterior angles.
(c) Identify a pair of alternate interior angles.
(d) Identify a pair of consecutive interior angles.
(e) Identify a linear pair.
(f) Identify a set of vertical angles.
24. Find the slope of the line that passes through the points:
(a) (1, 4) and (3, 2)
(b) (12, -2) and (-2, -16)
25. Can the lines be proven parallel? Is so, what theorem(s) would you use?
(a)
(b)
(c)
26. Solve to find the value of x. The lines shown are parallel. State which theorem you used.
(a)
(b)
Chapter 4 Triangle Conruence:
27. (a) Identify the congruent segments shown in the diagram.
(b)Identify the congruent angles shown in the diagram.
28. Classify the triangle by its angles and sides.
(a)
(b)
(c)
29. A triangle has side lengths of 2 cm and 5 cm. Give a possible side length for the third
side of the triangle.
30. In the following triangle, choose what side lengths could possible represent x, the third
side of the triangle.
Select ALL that apply:
(a) 18
(b) 3
(c) 5.5
(d) 2
(e) 11
31. Choose which postulate or theorem that can be used to prove the triangles congruent.
(a)
(b)
(c)
(d)
(e)
32. State the property used to mark the diagram.
̅̅̅̅ ≅ 𝐴𝐶
̅̅̅̅
(a) ACB ≅ ECD
(b) 𝐴𝐶
(f)
(c) A ≅ L
33. Write a 2-column proof to prove ARP ≅ LRN.
34. Write a 2-column proof to prove ABC ≅ CDA.
35. Solve for the missing angles in the triangles shown. Both triangles are isosceles.
(a) If mB = 46, find mA and mC
(b) Find the values for x and y.
Chapter 7 Transformations:
36. How many lines of symmetry does the following polygon have?
(a)
(b)
(c)
37. What does the coordinate notation mean when talking about a translation?
(a)(𝑥, 𝑦) → (𝑥 + 6, 𝑦 − 1)
(b) (𝑥, 𝑦) → (𝑥 − 15, 𝑦 − 7)
38. Name the type of transformation. Then name the coordinates of the image.
(a)
(b)
(c)
(d)
39. Perform the composition of point A and name the coordinate A’’. A(-3, 4)
(a) translation: (𝑥, 𝑦) → (𝑥 + 6, 𝑦 − 1)
(b) reflection over the y-axis
reflection over the x-axis
translation (𝑥, 𝑦) → (𝑥 − 1, 𝑦 + 2)