Download Marking Period 1 Review

Name: ____________________________________
Teacher: Mrs. Ferry
1. 2 3. 4 In the construction shown below, is drawn.
If two sides of a triangle have lengths of and , which
fraction can not be the length of the third side?
1. 2. 3. 4. 4. 2 Which statement is not always true when ∆ABC ≅ ∆XYZ?
In ∆ABC, 1. 2. 3. 4. is the
perpendicular bisector of side median to side altitude to side bisector of ∠ACB
1. ≅ 2. ≅ 3. ∠CAB ≅​ ∠​ZXY
4. ∠BCA ≅​ ∠​YZX
5. 1 In ∆ABC shown below, medians at point R.
, , and intersect
2. 3 Given:
bisects at C
and are drawn
∠ABC ≅ ​∠EDC
Which statement is needed to prove ∆ABC ≅​ ∆EDC using
ASA?
1. ∠
​ ABC and ​∠EDC are right angles.
2. bisects at C.
3. ∠BCA ≅ ​∠DCE
4. ∠DEC ≅​ ​∠BAC
If CR = 24 and RF = 2x − 6, what is the value of x?
1. 9 3. 15
2. 12 4. 27
6. 2 When the transformation T2,-1 is performed on point A, its
image is point A’(−3, 4). What are the coordinates of A?
1. (5,−5) 3. (−1,3)
2. (−5,5) 4. (−6, −4)
7. 3 In ∆ABC, m∠CAB = 2x and m∠​ACB = x + 30. If is
extended through point B to point D, m∠​CBD = 5x − 50. What
is the value of x?
1. 25 3. 40
2. 30 4. 46
8. 3 In the diagram below, || 10. 3 Consider triangle ABC graphed below:
. Transversal and line segment HF are drawn.
If m∠HFG = 130 and m∠EHF = 70, what is m∠ABE?
1. 40 3. 60
2. 50 4. 70
9. 4 As shown in the diagram below of ∆ABC, through D, m∠A = 70, and m∠​ACD = 115.
Which statement is true?
1. 2. 3. 4. AC > AB
AB > BC
BC < AC
AC < AB
is extended
Triangle ABC will be rotated 90° clockwise around the origin
and then reflected across the y-axis. Which additional
transformation(s) will map the image triangle back onto the
original triangle?
1. Rotate 270° clockwise around the origin.
2. Reflect across the line y = x.
3. Reflect across the line y = x, then rotate 180°
counterclockwise.
4. Rotate 180° clockwise around the origin.
11. 1 In the diagram below, at C.
bisects at B, and bisects 13. 3 In parallelogram QRST shown below, diagonal and V are points on intersects at W.
and is drawn, U
, respectively, and If m∠ S = 60°, m∠ SRT = 83°, and m∠ TWU = 35°, what is
m∠ WVQ?
Which statement is always true?
1. 37° 3. 72°
2. 60° 4. 83°
1. 2. ≅ ≅ 3. bisects at C.
4. bisects at B.
12. 3 Which transformation would result in the perimeter of a triangle
being different from the perimeter of its image?
1. (x,y) → (y,x)
2. (x,y) → (x,−​y)
3. (x,y) → (4x,4y)
4. (x,y) → (x + 2,y − 5)
14. 2 Which set of numbers could be the lengths of the sides of an
isosceles triangle?
1. {1, 1, 2} 3. {3, 4, 5}
2. {3, 3, 5} 4. {4, 4, 9}
15. 1 In ΔABC, m∠​​B < m∠​​A < m∠​​C. Which statement is false?
1. AC > BC
2. BC > AC
3. AC < AB
4. BC < AB
16. 2 What is the measure of each interior angle in a regular
octagon?
1. 108° 3. 144°
2. 135° 4. 1080°
17. 4 The lengths of two sides of a triangle are 7 and 11. Which
inequality represents all possible values for x, the length of the
third side of the triangle?
1. 4 ≤ x ≤ 18 3. 4 ≤ x < 18
2. 4 < x ≤ 18 4. 4 < x < 18
18. 2 The sum of the interior angles of a regular polygon is 720°.
How many sides does the polygon have?
1. 8 3. 5
2. 6 4. 4
19. 3 In quadrilateral ABCD, each diagonal bisects opposite angles. If m∠DAB = 70, then ABCD must be a
1. rectangle 3. rhombus
2. trapezoid 4. square
20. 1 What are the coordinates of the image of point A (2, -7) under the translation (x, y) → (x - 3, y + 5)?
1. (-1, -2) 3. (5, -12)
2. (-1, 2) 4. (5, 12)
21. 1 A sequence of transformations maps rectangle ABCD onto rectangle A″B″C″D″, as shown in the diagram below.
Which sequence of transformations maps ABCD onto A′B′​C′​D′ and then maps A′​B′​C′​D′ onto A″​B″​C″​D″?
1. 2. 3. 4. a reflection followed by a rotation
a reflection followed by a translation
a translation followed by a rotation
a translation followed by a reflection
22. 2 A parallelogram must be a rectangle when its
1. diagonals are perpendicular
2. diagonals are congruent
3. opposite sides are parallel
4. opposite sides are congruent
23. 1 Steve drew line segments ABCD, EFG, BF, and CF as shown in the diagram below. Scalene ∆BFC is formed.
Which statement will allow Steve to prove 1. 2. 3. 4. ?
∠CFG ≅ ∠FCB
∠ABF ​≅ ∠BFC
∠EFB ≅ ∠CFB
∠CBF ​≅ ∠GFC
24. 4 In the diagram below, line is parallel to line m, and line w is a transversal.
If m∠2 = 3x + 17 and m∠3 = 5x - 21, what is m∠1?
1. 19 3. 74
2. 23 4. 86
25. 2 A student used a compass and a straightedge to construct in ΔABC as shown below.
Which statement must always be true for this construction?
1. ∠CEA ≅ ∠CEB
2. ∠ACE ≅ ∠BCE
3. ≅ 4. ≅ 26. 2 In ΔCAT, m∠C = 65, m∠A = 40, and B is a point on side ​, such that ⊥
. Which line segment is shortest?
1. 2. 3. 4. 27. 3 In ΔFGH, m∠F = m∠H, GF = x + 40, HF = 3x – 20, and GH = 2x + 20. The length of 1. 20 3. 60
2. 40 4. 80
is
28. 2 In the diagram of Δ​PQR shown below, What is m m∠Q?
1. 44 3. 11
2. 40 4. 10
is extended to S, m∠P = 110, m∠Q = 4x, and m∠QRS = x2 + 5x.
29. 1 In the diagram below, point K is in plane P.
How many lines can be drawn through K, perpendicular to plane
P?
1. 1 3. 0
2. 2 4. an infinite number
30. 2 In the diagram below, ΔXYV ≅ ΔTSV.
Which statement can not be proven?
1. ∠XVY ≅​ ∠TVS
2. ∠VYX ≅​ ∠VUT
3. ≅ 4. ≅ 31. In the diagram below, The value of x is 5.
m∠RSU = 36
m∠UST = 36
m∠RST = 72
bisects ∠RST. Find x, m∠RSU, m∠UST and m∠RST.
32. If DF = 190, find the value of x. Then find DE and EF. The value of x is 20.
DE = 110
EF = 80
33. 3 Triangle ABC is shown in the diagram below.
If joins the midpoints of 1. DE = 2. and , which statement is not true?
CB
|| 3. 4. ΔABC ∼ ΔAED
34. 3 The diagram below shows the construction of an equilateral triangle.
Which statement justifies this construction?
1. 2. 3. 4. ∠A + ∠B + ∠C = 180
m∠A = m∠B = m∠C
AB = AC = BC
AB + BC > AC
35. 1 In the diagram below of ΔABC, ≅ , ≅ , and ≅ .
Point P must be the
1. centroid
3. incenter
2. circumcenter 4. orthocenter
36. The coordinates of the vertices of ΔRST are R(–2, 3), S(4, 4), and T(2, –2). Triangle R'S'T' is image of ΔRST after a rotation of
90° about the origin.
State the coordinates of the vertices of ΔR'S'T'.
[The use of the set of axes below is optional.]
Answer: R’(-3, -2), S’(-4, 4), T’(2, 2)
37. 4 The diagram below shows a pair of congruent triangles, with
∠ADB ≅ ∠CDB and ∠ABD ≅ ∠CBD.
Which statement must be true?
39. 1 In the accompanying diagram, Which statement is true?
1. 2. 3. 4. ⊥ and ⊥ m∠ 1 = m ∠ 3
m∠ 1 > m ∠ 3
m∠ 1 + m ∠ 2 + m ∠ 3 = 180
m∠ 1 + m ∠ 2 = m ∠ 3
1. ∠ADB ≅ ∠CBD
2. ∠ABC ≅ ∠ADC
3. ≅ 4. ≅ 38. 2 When a quadrilateral is reflected over the line y = x, which
geometric relationship is not preserved?
1. congruence 3. parallelism
2. orientation 4. perpendicularity
40. In the accompanying diagram of parallelogram DEFG, m ∠ E = 2x + 20 and m ∠ F = x + 10. Find the number of degrees in the
measure of angle G.
Answer: m ∠ G = 120
. 41. 4 In the diagram below of ΔGJK, H is a point on isosceles triangle and justify your answer.
1. 2. 3. 4. , ≅ , m∠G = 28, and m ∠ GJK = 70. Determine whether ΔGHK is an
Yes, because angles GKH and KGH are congruent. No, because angles GKH and KHJ are not congruent. Yes, because there are two congruent angles in triangle GHK.
No, because there are no two congruent angles in triangle GHK.
42. 4 In the diagram of ΔABC shown below, name the intersection of the three lines and the type of line shown in red.
1. 2. 3. 4. Orthocenter, created by the altitudes
Incenter, created by the angle bisectors
Centroid, created by the medians
Circumcenter, created by the perpendicular bisectors
43. 4 Triangle PQR has angles in the ratio of 2:3:5. Which type of triangle is ΔPQR?
1. acute
3. obtuse
2. isosceles 4. right
44. 2 Line segment AB is shown in the diagram below.
Which two sets of construction marks, labeled I, II, III, and IV, are part of the construction of the perpendicular bisector of line
segment AB?
1. I and II 3. II and III
2. I and III 4. II and IV
45. 2 Below is a construction for the angle ABC. What does the construction create?
1. 2. 3. 4. The perpendicular bisector of angle ABC.
The angle bisector of angle ABC.
The median of angle ABC.
The altitude of angle ABC. 46. 2 In the diagram below of quadrilateral ABCD with diagonal , m ∠ A = 93, m ∠ ADB = 43, m ∠ C = 3x + 5, m ∠ BDC = x + 19,
and m ∠ DBC = 2x + 6. If is parallel to , find m ∠ C. 1. 25° 3. 56°
2. 80° 4. 44°
47. The diagram below shows isosceles trapezoid ABCD with 5, find m ∠ BAD.
Answer: m ∠ BAD = 70
and ≅ . If m ∠ BAD = 2x and m ∠ BCD = 3x +
48. In the diagram below, quadrilateral STAR is a rhombus with diagonals and intersecting at E. ST = 3x + 30, SR = 8x − 5,
SE = 3z, TE = 5z + 5, AE = 4z − 8, m ∠ RTA = 5y − 2, and m ∠ TAS = 9y + 8. Find SR, RT, and m ∠ TAS.
SR: 51
RT: 90
m∠ TAS: 62
49. 3 The pentagon in the diagram below is formed by five rays.
52. 3 In which quadrant does the image of (4, -7) lie after the
translation that shifts (x, y) to (x - 6, y + 3)?
1. I 3. III
2. II 4. IV
53. 1 An exterior angle at the base of an isosceles triangle is always
1. obtuse
2. acute
3. greater than the sum of the base angles
4. equal to the sum of the base angles
54. 4 What is the image of (-2, 5) after a reflection in the origin?
1. (2, 5) 3. (-2, -5)
2. (5, 2) 4. (2, -5)
55. 1 In ΔRST, m ∠ R = 58 and m ∠ S = 72. Which is the shortest
side of the triangle?
What is the degree measure of angle x?
1. 72 3. 108
2. 96 4. 112
1. 2. 3. 50. 2 In the diagram, ABCD is a rectangle, E is a point on m∠ DAE = 30, and m∠ CBE = 20.
,
56. 3 The measure of the vertex angle of an isosceles triangle is three
times the measure of a base angle. Find the number of degrees
in the measure of the vertex angle.
1. 36 3. 108
2. 45 4. 215
57. 3 The point R(-2, 5) is reflected in the x-axis. In which quadrant
does the image of point R lie?
1. I 3. III
2. II 4. IV
What is m∠ x?
58. Triangle ABC has coordinates A(−1, 3), B(−6, 5), and C(−4,
7).
1. 25 3. 60
2. 50 4. 70
(a) The coordinates of ΔA' B'C', the image of ΔABC after a
reflection in the x-axis, are A'(-1, -3), B'(-6, -5), and C'(-4, -7).
51. 3 What is the image of (-4, -5) when reflected in the x-axis?
1. (5, -4) 3. (-4, 5)
2. (-5, -4) 4. (4, -5)
59. 4 If two sides of a triangle have lengths 4 and 9, then the length
of the third side may be any number
1. greater than 4 but less than 9
2. greater than 5
3. less than 13
4. greater than 5 but less than 13
(b) The coordinates of ΔA'' B''C'', the image of ΔABC after a
reflection in the line y = x, are A''(3, -1), B''(5, -6), and C''(7, -4).
(c) The coordinates of ΔA''' B'''C''', the image of ΔABC under
the translation which maps (x, y) to (x + 8, y + 3), are A'''(7, 6),
B'''(2, 8), and C'''(4, 10).
60. 3 The sum of the measures of the interior angles of a hexagon is
1. 360° 3. 720°
2. 540° 4. 1280°