geometry
<object:standard:ma.912.g.3.3>Two quadrilaterals EFGH and IJKL are drawn on a coordinate grid. The coordinates of the vertices of each quadrilateral are given below.
EFGH – E (1, 4), F (2, 4), G (2, 2), H (1, 2)
IJKL – I (-4, -1), J (-1, -1), K(-1, -7), L(-4, -7)
Which statement about the two quadrilaterals is true?
The side lengths of IJKL are three times the corresponding side lengths of EFGH.
The side lengths of IJKL are congruent to the corresponding side lengths of EFGH.
The side lengths of IJKL are not proportional to the corresponding side lengths of EFGH.
The side lengths of IJKL are half of the corresponding side lengths of EFGH.
Question 2 (Multiple Choice Worth 4 points)
(3.03 MC) <object:standard:ma.912.g.4.3>
The figure below shows two triangles that were constructed using a compass and straightedge. Justin used the ASA postulate to prove that triangle XYZ is congruent to triangle ABC.
As part of the proof Justin showed that side YZ is congruent to side BC. Using this congruency, which of these other steps would Justin have likely performed to prove that the two triangles are congruent by the ASA postulate?
Place the compass on Y and draw an arc that passes through X.
Place the compass on X and draw an arc to cross side XY at L and side ZX at M . Place the compass on L and set the width of the compass to segment LM.
Place the compass on X and set the width to side XZ. Place the compass on A and draw an arc to cross side AC at point C.
Place the compass on Z and draw an arc to cross side YZ at L and side ZX at M. Place the compass on L and set the width of the compass to segment LM.
Question 3 (Multiple Choice Worth 4 points)
(4.04 MC) <object:standard:ma.912.g.5.3>
The picture shows a portion of an irrigation system for a farm. LM is the main water pipe.
What is the length of the main water pipe LM?
19.1 feet
12.7 feet
5.5 feet
6.4 feet
Question 4 (Multiple Choice Worth 4 points)
(3.01 MC) <object:standard:ma.912.g.4.7>
Nancy cuts a piece of cardboard in the shape of a triangle. What could be the lengths of the three sides of the triangle?
2 cm, 4 cm, 7 cm
2 cm, 3cm, 4cm
2 cm, 3cm, 6cm
2 cm, 4 cm, 1 cm
Question 5 (Multiple Choice Worth 4 points)
(4.01 – 4.04 MC) <object:standard:ma.912.g.5.4>
The figure shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced.
What is the length of the wood that is needed to replace AD?
4.2 inches
5.7 inches
2.5 inches
1.3 inches
Question 6 (Multiple Choice Worth 4 points)
(4.03 MC) <object:standard:ma.912.t.2.1>
The height of a cell phone tower, AB, is 280 feet.
What is the distance, in feet, between the tip of the tower A and a point C on the ground?
280 sec 50°
280 sin 50°
Question 7 (Multiple Choice Worth 4 points)
(4.02 MC) <object:standard:ma.912.t.2.1>
The figure shows a triangular piece of cloth.
What is the length of the portion BC of the cloth?
5 cos 38°
5 sin 38°
Question 8 (Multiple Choice Worth 4 points)
(2.04 MC) <object:standard:ma.912.g.4.2>
Look at the acute triangle EFG in which O is the centroid and R is the orthocenter.
Which statement is true about the segments in triangle EFG?
Segment GR is two-thirds the length of segment GP.
Segment EP is the same length as segment PQ.
Segment GO is two-thirds the length of segment GQ.
Segment GQ is the same length as segment GP.
Question 9 (Multiple Choice Worth 4 points)
(5.01 LC) <object:standard:ma.912.g.3.1>
Which statement best describes a rhombus?
It has all four sides congruent.
It has adjacent sides unequal.
It has diagonals which intersect at 60°.
It has all angles measuring 90°.
Question 10 (Multiple Choice Worth 4 points)
(3.04 LC) <object:standard:ma.912.g.4.4>
Bill designs a table with a glass top.
What is the length of the side AB of the glass top?
20 inches
30 inches
32inches
36 inches
Question 11 (Multiple Choice Worth 4 points)
(2.03 MC) <object:standard:ma.912.g.1.1>
Look at the graph.
What is the length of segment KL?
5 units
8 units
12 units
13 units
Question 12 (Multiple Choice Worth 4 points)
(2.02 MC) <object:standard:ma.912.g.4.1>
Layla plotted points P, Q, and R to represent the vertices of a triangle as shown in the figure below.
What should Layla do to make triangle PQR a right isosceles triangle?
Move Q to a point on segment AB beyond the arc.
Move R to the point of intersection of segment AB and the arc.
Move R to the left of segment AB beyond the arc.
Move Q to the point of intersection of segment AB and the arc.
Question 13 (Multiple Choice Worth 4 points)
(5.05 HC) <object:standard:ma.912.g.3.3>
A quadrilateral EFGH is drawn on a coordinate grid as shown below.
Pamela will draw a quadrilateral IJKL similar to quadrilateral EFGH. The length of IJ should be 6 and I should be located at point (1, -3). At which points will vertices J and K be located?
J(1, -3) and ((11, -3)
J(1, 3) and K(9, 3)
J(7, 9) and K(5, 9)
J(3, 1) and K(3, 9)
Question 14 (Multiple Choice Worth 4 points)
(1.03 MC) <object:standard:ma.912.g.1.2>
The steps below describe the construction of a line AG which is parallel to segment PQ and passes through a point A above PQ.
In the next step an arc is drawn from point F which intersects the arc through F in point G. What statement is true for this step?
The width of the compass is equal to BE.
The width of the compass is equal to DE.
The width of the compass is equal to AE.
The width of the compass is equal to AF.
Question 15 (Multiple Choice Worth 4 points)
(5.02 MC) <object:standard:ma.912.g.3.1>
Which statement best describes a parallelogram and a kite?
A parallelogram has exactly one pair of opposite sides that are parallel and a kite has no parallel sides.
Both have at least two sides congruent.
Both have opposite pairs of sides parallel.
A parallelogram has opposite sides congruent and a kite has all sides congruent.
Question 16 (Multiple Choice Worth 4 points)
(3.02 MC) <object:standard:ma.912.g.4.4>
The two triangles shown below are congruent.
What is the value of x?
1
2
3
4
Question 17 (Multiple Choice Worth 4 points)
(2.01 MC) <object:standard:ma.912.g.4.1>
The chart below shows the angles of three triangles.
Name of triangle |
Measure of the angles |
Triangle 1 |
24°, 76°, 80° |
Triangle 2 |
45°, 45°, 90° |
Triangle 3 |
30°, 110°, 40° |
Which statement is correct?
Triangle 1 is an acute triangle and Triangle 2 is a right triangle.
Triangle 2 is a right triangle and Triangle 3 is an acute triangle.
Triangle 2 is an acute triangle and Triangle 3 is a right triangle.
Triangle 1 is an acute triangle and Triangle 3 is a right triangle.
Question 18 (Multiple Choice Worth 4 points)
(1.01 HC) <object:standard:ma.912.g.8.1>
Look at the planes ABCD and EFGH shown below.
Which statement is true about the two planes?
XY is the segment along which they intersect.
They intersect at exactly two points.
They intersect at exactly eight points and two lines.
C is the only point where they intersect.
Question 19 (Multiple Choice Worth 4 points)
(4.04 MC) <object:standard:ma.912.g.5.3>
Look at the figure.
What is the length of segment KM?
14.1 inches
17.3 inches
10 inches
20 inches
Question 20 (Multiple Choice Worth 4 points)
(4.01 – 4.04 MC) <object:standard:ma.912.g.5.4>
Two boats start their journey from the same point A and travel along directions AC and AD, as shown below.
What is the distance, CD, between the boats?
461.9 ft
530.9 ft
646.4 ft
325.5 ft
Question 21 (Multiple Choice Worth 4 points)
(1.04 MC) <object:standard:ma.912.g.1.3>
Look at the figure.
What is the measure of angle HLF?
35°
40°
50°
45°
Question 22 (Multiple Choice Worth 4 points)
(2.02 MC) <object:standard:ma.912.g.4.1>
As part of constructing a scalene triangle, Jordan drew a line segment and plotted one vertex of the triangle on the line segment. With this vertex as the center, Jordan drew an arc to create a 180 degree angle. How can Jordan ensure that the other two points he plots will represent the remaining two vertices of a scalene triangle?
Plot both the points on the line segment.
Plot one point on the arc and the other point beyond the arc.
Plot both points on the arc, one on the left and the other on the right.
Plot both the points beyond the arc.
Question 23 (Multiple Choice Worth 4 points)
(5.03 LC) <object:standard:ma.912.g.3.2>
Which statement is correct about a rhombus and a rectangle?
Both have two pairs of opposite sides parallel.
Both have four right angles.
Both have all four sides congruent.
Both have diagonals forming right angles.
Question 24 (Multiple Choice Worth 4 points)
(1.02 MC) <object:standard:ma.912.g.1.2>
The figure below shows some steps that Meg used to construct an angle bisector BO of an angle ABC.
In the next step Meg draws two arcs, one from point P and the other from point Q. Which of the following is true for this step?
The width of the compass is not the same while drawing the arcs from point P and point Q.
The width of the compass is adjusted to BQ to draw the arc from point P and BA to draw an arc from Q.
The width of the compass is the same while drawing the arcs from point P and point Q.
The width of the compass is adjusted to BC to draw the arc from point P and BP to draw an arc from Q.
Question 25 (Multiple Choice Worth 4 points)
(2.03 MC) <object:standard:ma.912.g.1.1>
Two end points of a line segment are (-8, 0) and (4, -2). What are the coordinates of the point on the line through which its bisector passes?
(-4, -2)
(-8, 2)
(-6, 1)
(-2, -1)
Question 26 (Multiple Choice Worth 4 points)
(2.05 MC) <object:standard:ma.912.g.4.2>
The figure below shows the incenter, M, of the triangle XYZ.
Which statement is always correct about the triangle XYZ?
Segment MN is congruent to segment XM.
Measure of angle XYM is equal to measure of angle NXZ.
Segment XZ is congruent to segment XM.
Measure of angle XZM is equal to measure of angle MZY.
Question 27 (Multiple Choice Worth 4 points)
(2.04 MC) <object:standard:ma.912.g.4.2>
Look at the triangle KLM.
Which statement is true about segments LN and MJ in triangle KLM?
Segments LN and MJ are the medians of triangle KLM.
LN is the median and MJ is the altitude of triangle KLM.
Segments LN and MJ are the altitudes of triangle KLM.
LN is the altitude and MJ is the median of triangle KLM.
Question 28 (Multiple Choice Worth 4 points)
(1.01-1.03 MC) <object:standard:ma.912.g.8.6>
Macy adjusts the width of her compass equal to PQ. Using the same width of the compass, she plans to draw an arc from point R, shown below.
What is Macy constructing?
a triangle with vertices at P, Q, and R
a segment from R that will be the perpendicular bisector to PQ
a segment from R that will have a length congruent to PQ
a square with sides PQ, QS, SR and RP
Question 29 (Multiple Choice Worth 4 points)
(3.01 MC) <object:standard:ma.912.g.4.7>
A triangular stage is to be built for a school event.
What could be the length of the side BC of the stage?
15 feet
100 feet
105 feet
10 feet
Question 30 (Multiple Choice Worth 4 points)
(1.04 MC) <object:standard:ma.912.g.1.3>
Look at the figure.
What is the value of x?
30
40
10
20
Question 31 (Multiple Choice Worth 4 points)
(2.05 MC) <object:standard:ma.912.g.4.2>
Look at the triangle ABC with E as its circumcenter.
Which line segment will pass through point E in the triangle ABC?
The line segment that bisects side BC at a right angle.
The line segment from angle B that is perpendicular to side AC.
The line segment from angle A that is perpendicular to side BC.
The line segment that bisects angle ACB and intersects side AB.
Question 32 (Multiple Choice Worth 4 points)
(5.03 MC) <object:standard:ma.912.g.3.2>
Look at the Venn diagram.
Which statement best fits the portion labeled X in the Venn diagram?
Has no congruent angles.
Does not have any congruent sides.
Diagonals are perpendicular.
Diagonals bisect each other.
Question 33 (Multiple Choice Worth 4 points)
(5.02 LC) <object:standard:ma.912.g.3.1>
Which statement is correct about a trapezoid?
It has four equal sides.
It is called an isosceles trapezoid if its legs are equal.
It is called an isosceles trapezoid if it has one pair of adjacent sides that are equal.
It has two pairs of opposite sides that are equal and parallel.
Question 34 (Multiple Choice Worth 4 points)
(5.04 MC) <object:standard:ma.912.g.3.3>
Nathan is drawing a square ABCD on a coordinate grid. He plotted three vertices of the square at A (4, -9), B (4, 3), and C (16, 3). Where should he plot point D to make the square?
(16, 15)
(-16, 9)
(-16, -15)
(16, -9)
Question 35 (Multiple Choice Worth 4 points)
(3.05 MC) <object:standard:ma.912.g.5.2>
Three yachts are anchored on the harbor as shown below.
How far is Yacht 2 from the harbor?
10 feet
81 feet
90 feet
9 feet
Question 36 (Multiple Choice Worth 4 points)
(4.03 MC) <object:standard:ma.912.t.2.1>
The picture shows a box sliding down a ramp.
What is the distance, in feet, that the box has to travel to move from point A to point C?
10 cosec 62°
10 sin 62°
Question 37 (Multiple Choice Worth 4 points)
(5.04 HC) <object:standard:ma.912.g.3.3>
Points P (-6, 4), Q (-4, 4), R (-4, 2), and S (-6, 2) are plotted on a coordinate grid. Which statement is correct about the points?
They form a square because diagonals PR and QS are congruent.
They do not form a square because the opposite sides are not parallel.
They form a square because PR is perpendicular to RS.
They do not form a square because the sides of quadrilateral PQRS are not congruent.
Question 38 (Multiple Choice Worth 4 points)
(2.01 LC) <object:standard:ma.912.g.4.1>
Which statement best describes an equilateral triangle?
It has all sides of different lengths.
It has at least two angles of same measure.
It has all sides of same length.
It has all angles of different measures.
Question 39 (Multiple Choice Worth 4 points)
(3.04 MC) <object:standard:ma.912.g.4.4>
A pole that is 20 feet tall casts a shadow 48 feet long. At the same time, another pole casts a shadow having a length of 12 feet. What is the height, in feet, of the second pole?
28.8
80
5
8.5
Question 40 (Multiple Choice Worth 4 points)
(3.04 MC) <object:standard:ma.912.g.4.5>
The figure below shows a triangular lawn labeled PQR. There are two fences, AB and BC.
What is the total length of the fence AB and BC?
64 feet
80 feet
62 feet
74 feet
Question 41 (Multiple Choice Worth 4 points)
(1.02 MC) <object:standard:ma.912.g.1.2>
Some steps to construct an angle MNT congruent to angle PQR are listed below. Step 3 is not listed.
Step 1 - Draw a segment NT.
Step 2 - Use a compass to draw an arc from point Q which intersects the side PQ of angle PQR at point A and the side QR at point B.
Step 3 -
Step 4 - Adjust the width of the compass to AB and draw an arc from point X such that it intersects the arc drawn from N in a point Y.
Step 5 - Join points N and Y using a straightedge.
Which statement describes step 3 correctly?
Use the same width of the compass to draw an arc from point T, which intersects the segment NT at a point X.
Use the same width of the compass to draw an arc from point N which intersects the segment NT at a point X.
Use the same width of the compass to draw an arc from point A, which intersects the segment NT at a point X.
Use the same width of the compass to draw an arc from point B, which intersects the segment NT at a point X.
Question 42 (Multiple Choice Worth 4 points)
(3.05 MC) <object:standard:ma.912.g.5.2>
When an altitude is drawn to the hypotenuse of a right triangle, the lengths of the segments of the hypotenuse are 9 and 36. What is the length of the altitude?
6
18
45
3
Question 43 (Multiple Choice Worth 4 points)
(3.04 LC) <object:standard:ma.912.g.4.5>
Look at the triangle shown below.
What is the length of the segment PD?
14 cm
8 cm
10 cm
12 cm
Question 44 (Multiple Choice Worth 4 points)
(3.02 LC) <object:standard:ma.912.g.4.4>
The figure below shows triangle MNO congruent to triangle PQR.
Which of the following is correct?
The length of MN is equal to 10 cm.
The length of MN is equal to 12 cm.
The length of NO is equal to 12 cm.
The length of NO is equal to 10 cm.
Question 45 (Multiple Choice Worth 4 points)
(5.01 MC) <object:standard:ma.912.g.3.1>
Which statement best compares a square and a rhombus?
A rhombus has all angles equal to 90° but a square has opposite angles equal.
A rhombus has diagonals which are unequal but a square has diagonals which are equal.
A rhombus has equal diagonals but a square has unequal diagonals.
A rhombus has non perpendicular diagonals but a square has perpendicular diagonal.
Question 46 (Multiple Choice Worth 4 points)
(4.02 MC) <object:standard:ma.912.t.2.1>
A lamp post, CAB, bent at point A after a storm. The tip of the lamp post touched the ground at point C, as shown below.
What is the height, in feet, of the portion AB of the lamp post?
12 tan 45°
12 cos 45°
solution
body preview (111 words)
16)
i) x
17)
i)Triangle 1 xx xx xxxxx xxxxxxxx xxx Triangle x xx x right xxxxxxxxx
xxx
xxxx XY is xxx segment along which they xxxxxxxxxx
xxx
xxx xx inches
20)
xx xxxxx xx
21)
ii) xx
22)
xxxx xxxx xxxx the points xx xxx line segment.
23)
xxxxx xxxx have xxxxxxxxx xxxxxxx xxxxx angles.
25)
iv) xxxx -1)
29)
xxx 100 xxxx
xxx
ii) 40
xxx
xxx (16,-9)
xxx
xxxx 90
xxx
xx xxxx form a square xxxxxxx diagonals PR and xx are xxxxxxxxxx
xxx
iii) It has all sides of xxxx xxxxxxx
xxx
iii) 5
xxx
xxxxxx xx feet
41)
ii)Use the same width xx the compass to xxxx xx arc from xxxxx N xxxxx xxxxxxxxxx the segment NT at a point X.
xxx
i) 6
xxx
xxx 12 xx
44)
iii) xxx xxxxxx of xx is xxxxx xx xx cm.
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