Midterm Review Packet Name: _______________ 1. What is the slope of a line perpendicular to the line whose equation is ? 1) 2) 3) 4) 2. What is the equation of a line passing through and parallel to the line represented by the equation ? 1) 2) 3) 4) 3. A line segment has endpoints and . What are the coordinates of the midpoint of ? 1) 2) 3) 4) 4. Point M is the midpoint of . If the coordinates of A are and the coordinates of M are , what are the coordinates of B? 1) 2) 3) 4) 5. Find, in simplest radical form, the length of the line segment with endpoints whose coordinates are and .
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Midterm Review Packet Name: _______________
1. What is the slope of a line perpendicular to the line whose equation is ? 1)
2)
3)
4)
2. What is the equation of a line passing through and parallel to the line represented by the
equation ? 1)
2)
3) 4)
3. A line segment has endpoints and . What are the coordinates of the midpoint of ?
1) 2) 3) 4)
4. Point M is the midpoint of . If the coordinates of A are and the coordinates of M are , what are the coordinates of B?
1) 2) 3) 4)
5. Find, in simplest radical form, the length of the line segment with endpoints whose coordinates are and .
2
6. Which illustration shows the correct construction of an angle bisector? 1)
3)
2)
4)
7. Which diagram shows the construction of the perpendicular bisector of ? 1)
2)
3)
4)
3
8. Which geometric principle is used to justify the construction below?
1) A line perpendicular to one of two parallel
lines is perpendicular to the other. 2) Two lines are perpendicular if they intersect
to form congruent adjacent angles. 3) When two lines are intersected by a
transversal and alternate interior angles are congruent, the lines are parallel.
4) When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel.
9. Which diagram shows the construction of an equilateral triangle?
4
10. In , , , and . Which type of triangle is ?
1) right 2) scalene 3) isosceles 4) equilateral
11. Tina wants to sew a piece of fabric into a scarf in the shape of an isosceles triangle, as shown in the accompanying diagram.
What are the values of x and y? 1) 2) 3) 4)
12. In the diagram below of , side is extended to point D, , , and .
What is ? 1) 5 2) 20 3) 25 4) 55
5
13. Phil is cutting a triangular piece of tile. If the triangle is scalene, which set of numbers could represent the lengths of the sides?
1) 2) 3) 4)
14. On the banks of a river, surveyors marked locations A, B, and C. The measure of and the measure of .
Which expression shows the relationship between the lengths of the sides of this triangle? 1) 2) 3) 4)
15. The diagram below shows the construction of the center of the circle circumscribed about .
This construction represents how to find the intersection of 1) the angle bisectors of 2) the medians to the sides of 3) the altitudes to the sides of 4) the perpendicular bisectors of the sides of
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16. In shown below, P is the centroid and .
What is the length of ? 1) 6 2) 9 3) 3 4) 12
17. The measures of five of the interior angles of a hexagon are 150°, 100°, 80°, 165°, and 150°. What is the measure of the sixth interior angle?
1) 75° 2) 80° 3) 105° 4) 180°
18. One piece of the birdhouse that Natalie is building is shaped like a regular pentagon, as shown in the accompanying diagram.
If side AE is extended to point F, what is the measure of exterior angle DEF? 1) 36° 2) 72° 3) 108° 4) 144°
7
19. The measure of an interior angle of a regular polygon is 120°. How many sides does the polygon have?
1) 5 2) 6 3) 3 4) 4
20. If point is rotated counterclockwise 90° about the origin, its image will be point 1) 2) 3) 4)
21. What is the image of point after a reflection in the x-axis? 1) 2) 3) 4)
22. The image of point when reflected in the y-axis is 1) 2) 3) 4)
23. What are the coordinates of point P, the image of point after a reflection in the line ? 1) 2) 3) 4)
24. What is the image of point under a R180°? 1) 2) 3) 4)
8
25. A translation moves to . What are the coordinates of the image of point under
the same translation? 1) 2) 3) 4)
26. What is the image of point after the composition of transformations defined by ry=x followed by a R90°?
1) 2) 3) 4)
27.A transformation of a polygon that always preserves both length and orientation is 1) dilation 2) translation 3) line reflection 4) glide reflection
27. When a dilation is performed on a hexagon, which property of the hexagon will not be preserved in its image?
1) parallelism 2) orientation 3) length of sides 4) measure of angles
28. What is the image of after a translation of 3 units right and 7 units down? 1) 2) 3) 4)
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29. As shown in the diagram below, is a median of .
Which statement is always true? 1) 2) 3) 4)
30. Given: , is the perpendicular bisector of
Which statement can not always be proven? 1) 2) 3) 4)
31. In the diagram below of and , , and .
To prove that and are congruent by SAS, what other information is needed? 1) 2) 3) 4)
10
32. In the diagram of quadrilateral ABCD, , , and diagonal is drawn.
Which method can be used to prove is congruent to ? 1) AAS 2) SSA 3) SAS 4) HL
33. In the diagram below, .
Which statement must be true? 1) 2) 3) 4)
34. In the diagram below of , .
Using this information, it could be proven that 1) 3) 2) 4)
11
35. Given: bisects at E. Prove:
36. Given: , bisects , Prove:
37. Given: and , C is the midpoint of and Prove:
12
38. Construct the median of ∆ABC to AC .
39. Construct the altitude of ∆ABC to AC .
C
B
A
C
B
A
13
40. In the diagram below of , , , and .
Point P must be the 1) centroid 2) circumcenter 3) incenter 4) orthocenter
41. Which geometric principle is used in the construction shown below?
1) The intersection of the angle bisectors of a triangle is the center of the inscribed circle.
2) The intersection of the angle bisectors of a triangle is the center of the circumscribed circle.
3) The intersection of the perpendicular bisectors of the sides of a triangle is the center of the inscribed circle.
4) The intersection of the perpendicular bisectors of the sides of a triangle is the center of the circumscribed circle.
14
42. Triangle ABC has vertices , , and . Determine the point of intersection of the medians, and state its coordinates. [The use of the set of axes below is optional.]
43. What is the image of the point under the translation along the vector 4,3 − ? 1) 2) 3) 4)
44. Find the coordinates of the point P that lies along the directed line segment from A(1, 2) to B(10, 8) and partitions the segment in the ratio 2 to 1.
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45. Find the coordinates of the point P that lies along the directed line segment from C(-3, -1) to D(7, 6) and partitions the segment in the ratio 3 to 2.
46. The diagram at right shows the intersection of three lines concurrent at the ______________ of a triangle.
1)incenter 2) circumcenter 3) centroid 4) orthocenter
47. For a triangle, which two points of concurrence could be located outside the triangle?
1) incenter and centroid 2) centroid and orthocenter 3) incenter and circumcenter 4) circumcenter and orthocenter
48. Which point is equidistant from the three sides of the triangle?
1) circumcenter (2) incenter (3) centroid (4) orthocenter
16
49. When CDllAB and cut by transversal EF , 30+=∠ xBGH and xxDHG 42 +=∠ . Find x.
50.
H
GA B
C D
F
E
17
51. Which transformation is not a rigid motion? 1) Line reflection 2) Dilation 3) Rotation 4) Translation
52. The coordinates of are , , and . What are the coordinates of the vertices
of its image after the transformation?
1) 2) 3) 4)
53.
54.
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55. What are the coordinates of the point under the dilation ? 1) 2) 3) 4)
56. If the image of A after a dilation of is , what are the coordinates of A? 1) 2) 3) 4)
57. In which quadrant would the image of point fall after a dilation using a factor of ? 1) I 2) II 3) III 4) IV Transformations with Pictures
58. In the diagram below, under which transformation is the image of ?
1) 2) 3) 4)
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59. In the diagram below, under which transformation is the image of ?
1) dilation 2) reflection 3) rotation 4) translation
60. In the diagram below, which transformation was used to map to ?
1) dilation 2) rotation 3) reflection 4) glide reflection
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61. The line 4𝑦𝑦 + 3𝑥𝑥 = 15 is transformed by a dilation centered at the origin by a factor of 3. What is the equation its image?
62. Given ∆𝐴𝐴𝐴𝐴𝐴𝐴 ≅ ∆𝑋𝑋𝑋𝑋𝑋𝑋, describe a precise sequence of rigid motions that would map ∆𝐴𝐴𝐴𝐴𝐴𝐴 onto ∆𝑋𝑋𝑋𝑋𝑋𝑋.
21
63. Line is transformed by a dilation with a scale factor of 2 and centered at . The line's image is
1)
2)
3)
4)
64. In the diagram below, the vertices of are the midpoints of the sides of equilateral triangle ABC, and the perimeter of is 36 cm.
What is the length, in centimeters, of ? 1) 6 2) 12 3) 18 4) 4
65.
66. In the diagram of below, , , and . Find the perimeter of the triangle formed by connecting the midpoints of the sides of .
22
The night before Review:
1. Write the equation of a line that passes through the point (15, -6) and is perpendicular to the line 5x – 3y = 12.
2. Find the slope, midpoint, and length of AB. A(-2, 7) & B(6, 10)
3. M(2, -5) is the midpoint of AB. If A is located at (4, 12), find the coordinates of point B.
4. A(-8, 7) & B(7, -3) Point P partitions segment AB into a 3:7 ratio. Find point P
5. Given a regular Octagon:
a) Find the sum of the interior angles b) Find the measure of one interior angle c) Find the measure of one exterior angle d) Find the sum of the exterior angles
6. Given Point D(2, 4)
a) rx-axis b) ry-axis c) ry = x d) T-2, 5 e) R90° f) R180° g) D-3
7. Dilate the 5x – 7y = 35 by a scale factor of 4
8. Solve: a) x2 + 5x – 36 = 0 b) x2 – 3x – 40 = 0 c) x2 – 6x – 27 = 0
d) x2 + 8x + 12 = 0 e) x2 – 5x – 50 = 0 f) x2 + 3x – 180 = 0
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