Download Name_________________________________ PARCC Review 1

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PARCC Review
1. Select the drop-down menus to correctly complete each sentence.
The set of all points in a plane that are equidistant from a given point is called a
The given point is called the
Radius
Area
Center
Perimeter
2. Select from the drop-down to correctly complete each sentence. Given distinct noncollinear points A,
B, and C, the set of all points between A and C including A and C is
3. Which geometric figures have a measurable quantity?
Select each correct answer.
A.
line
B. angle
C. point
D. line segment
E. ray
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̅̅̅̅ one is one of those
4. Using a compass and a straightedge, a student constructed a triangle in which 𝑋𝑌
sides.
The compass is opened to a set length and two intersecting arcs are drawn above ̅̅̅̅
𝑋𝑌 using X and
Y as the centers. The intersection of the two arcs is labeled as a point Z.
Part A
What could be the set length of the compass so that is ∆𝑋𝑌𝑍 is isosceles but not equilateral?
Select all that apply
A.
less than ½ XY
B.
equal to ½ XY
C.
between ½ XY and XY
D.
equal to XY
E.
greater than XY
Part B
Select the correct phrase to complete the sentence
If the opening of the compass is
then ∆𝑋𝑌𝑍 will be equilateral
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5. Jericho is making several constructions based on the segment shown.
Part A
For his fist construction, Jericho made the markings shown with a compass open to a length less
̅̅̅̅ . Jericho’s markings are useful for the construction of which of
than the length of segment 𝑃𝑄
the figures listed?
Select all that apply
A.
a 60° angle
B.
̅̅̅̅
a bisector of 𝑃𝑄
C.
line perpendicular to ̅̅̅̅
𝑃𝑄
D.
a rhombus with ̅̅̅̅
𝑃𝑄 as one diagonal
E.
an equilateral triangle with side ̅̅̅̅
𝑃𝑄
Part B
The first steps of Jericho’s second’s construction are shown. After drawing arcs from point 𝑆 and
point 𝑅, he adjusted the compass length using the intersection of the arc from point 𝑆 with
̅̅̅̅
⃗⃗⃗⃗⃗ . Which figure is he constructing?
𝑃𝑄 and 𝑆𝑅
̅̅̅̅̅through point R
A. the bisector of 𝑃𝑄
B. an angle congruent to∠𝑅𝑃𝑄 with vertex R
̅̅̅̅̅
C. a line through point R that is parallel to 𝑃𝑄
D. a circle containing points P, Q ,and R
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6. Quadrilateral ABCD is shown graphed in the 𝑥𝑦- coordinate plane.
Part A
Quadrilateral ABCD will be translated according to the rule (𝑥, 𝑦) → (𝑥 + 3, 𝑦 − 4) to form
A’B’C’D’.
Select the correct orientation of A’B’C’D’ and place it correctly on the plane.
Part B
Quadrilateral ABCD maps onto A”B”C”D”. It will undergo a different transformation that will
map 𝐴(−6,3) to A”, B(-4,5) to B”, C (-1,6) to C” , and D (-3,2) to D” .The transformation will
consist of a reflection over the y-axis followed by a translation. Point D” is shown plotted in the
plane after the transformation.
Plot the point A” in the plane.
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7. Part A
Line 𝑙 passes through the points (−4, −7) and (2, −3) on the coordinate plane.
Line 𝑚 passes through the points (−4, 1) and (2, 𝑤).
For what value of w is line m parallel to line 𝑙?
Enter your answer in the box.
Part B
Given the figure, write the expression that can replace 𝑡 and will guarantee that lines 𝑗 and 𝑘 are
parallel. Support your answer.
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8. The diagram shows regular hexagon ABCDEF with center at O.
Justine made these claims.

The only lines of symmetry for regular hexagon ABCDEF are the lines that contain one
vertex and O.

The only angle of rotation that shows rotational is 120°
Explain why Justine is correct or incorrect.
Enter your explanation is the space provided.
9. Triangle JKL will undergo a transformation to create triangle J’K’L’ in the 𝑥𝑦- coordinate plane.
Which transformations will result in ∆𝐽𝐾𝐿 ≅ ∆𝐽′ 𝐾 ′ 𝐿′ ?
A. (𝑥 , 𝑦)  (−𝑥, −𝑦)
B. (𝑥, 𝑦)  (−𝑥 , 𝑦)
C. (𝑥, 𝑦)  (𝑥, 𝑦 − 5)
D. (𝑥, 𝑦)  (𝑥 + 3, 𝑦 – 5)
E. (𝑥, 𝑦) (2𝑥, 3𝑦)
F. (𝑥, 𝑦)  (−𝑥, 𝑦 + 3)
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10. In the figure, 𝑝 ǁ 𝑞. Transversals 𝑡 and 𝑤 intersect at point 𝐿.
Part A
What is the missing reason in step 3?
A. Alternate interior angles along parallel lines
are congruent.
B. Alternate exterior angles along parallel lines
are congruent.
C. Corresponding angles along parallel lines are congruent
D. Vertical angles are congruent
Part B
Consider the proof of 𝑝 ‖ 𝑞 given that ∆ 𝐿𝐻𝐾 ~ ∆ 𝐿𝐽𝑍. If ∆ 𝐿𝐻𝐾 ~ ∆ 𝐿𝐽𝑍, then ∠𝐿𝐻𝐾 ≅ ∠𝐿𝐽𝑍 because
corresponding angles in similar triangles are congruent.
Which statement concludes the proof?
A.
If ∠𝐿𝐻𝐾 ≅ ∠𝐿𝐽𝑍 then 𝑝 ‖ 𝑞 because when base angles are congruent, the lines are parallel.
B.
If ∠ 𝐿𝐻𝐾 ≅ ∠𝐿𝐽𝑍 then 𝑝 ‖ 𝑞 because when corresponding angles are congruent, the lines are
parallel
C.
If ∠𝐿𝐻𝐾 ≅ ∠𝐿𝐾𝐻 then 𝑝 ‖ 𝑞 because when alternate exterior angles are congruent, the lines
are parallel
D.
If ∠𝐽𝐿𝑍 ≅ ∠𝐻𝐿𝐾, then 𝑝 ‖ 𝑞 because when corresponding angles are congruent the lines are
parallel
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11. Triangle 𝐴𝐵𝐶 is shown in the 𝑥𝑦- coordinate plane. The triangle will be translated 2 units down and
3 units right to create triangle 𝐴’𝐵’𝐶’. Indicate whether each of the listed parts of the image will or
will not be the same as the corresponding part in which the preimage (triangle 𝑨𝑩𝑪) by selecting
the appropriate box in the table.
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12. The right triangle in the coordinate plane is rotated 270° clockwise about the point (2, 1) and then
reflected across the 𝑦 −axis to form triangle A’B’C. Draw in the appropriate orientation for triangle
A’B’C into the correct position on the coordinate plane (sketch it).
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13. Triangle ABC is graphed in the xy- coordinate plane, as shown.
Part A
Triangle ABC is reflected in the x- axis to form triangle A”B”C”.
What are the coordinates of C’ after the reflection?
A.
(-6, 4)
B. (3, -2)
C. (4, -6)
D. (6, -4)
Part B
Triangle ABC in the xy- coordinate plane will be rotated 90 degrees counterclockwise about
point A to form triangle A”B”C”. Which graph represents A”B”C”?
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14. An incomplete proof of the theorem that the sum of the interior angles of a triangle is 180
degrees
is shown.
Part A
What is the appropriate reason for the statement in step 1?
A. Through any two points, there is exactly one line
B. Though a point not on a line, there is exactly one line parallel to the given line
C. If two lines cut by a transversal form congruent corresponding angle, then the lines are
parallel.
D. If two lines cut by a transversal form congruent alternate interior angles, then the lines are
parallel.
Part B
Which pairs of angles congruence or equalities should be used for the statement in step 2?
Indicate all such pairs.
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Part C
Select from the drop down menu to correctly complete the sentence.
The reason for the statement in step 2 is that
Part D
Select from the drop down menu to correctly complete the sentence. The appropriate reason
for the statement in step 5 is the
15. Octagon PQRSTVWZ is a regular octagon with its center at point C.
Which transformations will map octagon PQRSTVWZ onto itself?
Select each correct transformation
̅̅̅̅
A. reflecting over 𝑄𝑉
̅̅̅̅̅
B. reflecting over 𝑅𝑊
̅̅̅̅
C. reflecting over 𝑇𝑍
D. rotating 45° clockwise around point Z.
E. rotating 135° clockwise around point C
F. rotating 90° counterclockwise around point C.
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16. Part A
∆ABC meets the given criteria

The perimeter of triangle ABC is 50 units,

Only two of the sides have the same length

The third side is 16 units long, given in the diagram
What are the coordinates of point C that will meet the criteria for triangle ABC?
A. ( 6.25,8 )
B. ( 8, 6.25 )
C. ( 8, 15 )
D. ( 15, 8 )
Part B
Point C is placed at (12, 16) and point B is moved along the x-axis. Triangle ABC is still an
isosceles triangle and point A is still at the
origin. What is the new perimeter of ∆𝐴𝐵𝐶?
Provide valid mathematical reasoning and
calculations to support your answer.
Enter your answer, your reasoning, and your
calculations in the space provided
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17. Given: In ∆𝐴𝐵𝐶 shown, ̅̅̅̅
𝐵𝐴 ≅ ̅̅̅̅
𝐵𝐶
Part A
Select from the drop down menus to correctly complete step 2 of the proof.
Part B
Select from the drop down menus to correctly complete step 4 of the proof.
Part C
Select from the drop-down menus to correctly complete step 5 of the proof.
because of
Part D
What is the correct reason for the statement in step 6?
A. The transitive property of congruence
B. base angles of isosceles triangles are congruent
C. corresponding parts of congruent triangles are congruent
D. vertical angles are congruen
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18. In the diagram, quadrilaterals 𝐹𝐵𝐴𝐺 and 𝐶𝐷𝐸𝐹 are rectangles
How long is ̅̅̅̅
𝐷𝐸 rounded to the nearest tenth?
Enter your answer in the box.
19. Triangle ABC has sides with lengths of 3, 6 and 8. Classify each of the transformations described as
producing a triangle similar to triangle not similar to triangle ABC.
Drag and drop each transformation into the appropriate box.
20. Point A is located at -3, and point B is located at 19.
Select a point on the number line between A and B such that the distance from A to the point is
3
11
of
the distance from A to B.
Select a point on the number line to plot the point.
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21. A computer monitor is 20 inches wide. The aspect ratio, which is the ratio of the width of the screen
to the height of the screen, is 16:9. What is the length of the diagonal of the screen, to the nearest
whole inch?
Enter your answer in the box
22. In the xy- coordinate plane shown, line 𝑙 passes through point C and has a slope of -2.
Enter your answers in the boxes:
A dilation of line 𝑙 with center 𝐴 and a scale factor of 3 will
produce a new line through point C’, the image of point C
with coordinates (
slope of
,
) and with a
.
Hint – create a line segment
and dilate it. (1,0) is another
point on line 𝑙. Create another
triangle from on the point of
dilation.
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23. Triangle 𝑃 is dilated from center A by a scale factor of 2 to form triangle Q. The vertici\es from
triangle P are (-2,1), (2,4) and (2,1). The vertices for triangle Q are (-1,-3), (7,3) and (7,-3). Graph
point A, the center of the dilation.
Select the place on the coordinate plane to plot the point.
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24. ∆𝐴𝐵𝐶 is dilated from the center 𝐴 by a factor not equal to 1 to form ∆𝐴𝐾𝐿. Which of the
statements must be true?
Select all that apply.
A. ̅̅̅̅
𝐴𝐵 and ̅̅̅̅
𝐴𝐾 lie on the same line.
B. The line containing ̅̅̅̅
𝐵𝐶 is parallel to the line containing ̅̅̅̅
𝐾𝐿 .
C. ∠𝐴𝐵𝐶 ≅ ∠𝐴𝐶𝐵
D. ∠𝐴𝐵𝐶 ≅ ∠𝐴𝐾𝐿
E. ∆𝐴𝐵𝐶~∆𝐴𝐾𝐿
F. ∆𝐴𝐵𝐶 ≅ ∆𝐴𝐾𝐿
̅̅̅̅̅̅ graphed on a coordinate plane.
25. The diagram shows 𝑀𝑁
Point P lies on ̅̅̅̅̅̅
𝑀𝑁 and is ¾ of the way from M to N. What are the coordinates of point P?
26. The figure shows line segment JK and a point P that is not collinear with points J
and K.
Suppose that line segment J’K’ is the image of line segment JK after a dilation with
scale factor of 0.5 that is centered a point P. Which statement best describes the
position of line segment J’K’?
A.
Line segment J’K’ is parallel to line segment JK
B. Line segment J’K’ is perpendicular to line segment JK.
C.
Line segment J’K’ intersects line segment JK at one point, but is not perpendicular to
line segment JK.
D. Line segment J’K’ lies on the same line as line segment JK.
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27. Triangle 𝐴𝑃𝑄 is the image of ∆𝐴𝐵𝐶 under a dilation centered at vertex A with scale factor ½.
Triangle 𝑅𝐵𝑇 is the image of ∆𝐴𝐵𝐶 under a dilation centered at vertex B with scale factor ¾. Which
statement about ∆𝐴𝐵𝐶, ∆𝐴𝑃𝑄, and∆ 𝑅𝐵𝑇 is correct?
A. All these triangles are similar
B. None of the triangles are similar
C. Triangles APQ and RBT are not similar because they were dilated using different scale
factors.
D. Triangles APQ and RBT are not similar because they were dilated with different centers
of dilation.
28. A dilation of a center P (0, 0) and a scale factor 𝑘 is applied to ̅̅̅̅̅
𝑀𝑁. Let ̅̅̅̅̅̅
𝑀’𝑁’ represent the image of
̅̅̅̅̅
𝑀𝑁 after the dilation.
Select each correct statement.
A.
If 𝑘 > 0, then 𝑀’𝑁’ > 𝑀𝑁
B.
If 𝑘 > 1, then 𝑀’𝑁’ > 𝑀𝑁
C.
If 0 < 𝑘 < 1, then 𝑀’𝑁’ < 𝑀𝑁
D.
If 0.5 < 𝑘 < 1.5, then 𝑀’𝑁’ < 𝑀𝑁
E.
If 𝑘 = 1, then 𝑀’𝑁’ = 𝑀𝑁
F.
If 𝑘 = 0.5, then 𝑀’𝑁’ = 0.5( 𝑀𝑁 )
29. Given the two triangles shown, find the value of x.
Select from the drop-down menu to correctly complete the sentence.
The value of x is
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30. Points X and Z are on a number line, and point Y partitions ̅̅̅̅
𝑋𝑍 into two parts so that the ratio of the
length of ̅̅̅̅
𝑋𝑌 to the length of ̅̅̅̅
𝑌𝑍 is 5:7. The coordinate of X is 1.3 and the coordinate of Y is 3.8.
What is the coordinate of Z?
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