Geometry .. need it aced ! need it passed b or an a …

Question 1 (Multiple Choice Worth 4 points)

(4.02 MC) <object:standard:ma.912.t.2.1>
The diagram below shows the map of a mine. 

a right triangle ABC is drawn. Angle ABC measures 90 degrees. Length of AB is 4 km. The angle the tip of the mine shaft makes with the ground above is 18 degrees. 

How deep is the mine shaft?




Question 33 (Fill-In-The-Blank Worth 4 points)

(07.05 MC) <object:standard:ma.912.g.7.7>

A cylinder labeled X has a height of 16 inches and a radius of 10 inches. Another cylinder labeled Y has a height of 32 inches and a radius of 20 inches.

The volume of cylinder Y is _______ times the volume of cylinder X.

Answer for Blank 1: [removed]



Question 34 (Fill-In-The-Blank Worth 4 points)

(07.01 MC) <object:standard:ma.912.g.4.4>

The figure below shows CB = 4, BE = 5, AB = x – 4, and DB = x + 3. 

Triangle ABC is a right triangle with measure of angle ACB equal to 90 degrees. The measure of side CB is 4 and AB is x minus four. D is a point on the left of C on BC extended. A point E is labeled on AB such that DE is perpendicular to AB. Measure of EB is 5 and DB is x plus 3.

If △ABC ~ △DBE, the value of x is _________

Answer for Blank 1: [removed]



Question 35 (Multiple Choice Worth 4 points)

(07.05 MC) <object:standard:ma.912.g.7.6>

Two similar solids are shown below.

Two similar solids are shown. The length of the smaller solid is 4 feet and its volume is 512 cubic feet. The length of the bigger solid is 6 feet. Its volume is not known.

What is the volume of the larger solid?

[removed] 2048 ft3

[removed] 1024 ft3

[removed] 4096 ft3

[removed] 6042 ft3



Question 36 (Multiple Choice Worth 4 points)

(3.01 MC) <object:standard:ma.912.g.4.7>
A carpenter proposes to make 4 triangular shelves of the following dimensions: 

Shelf 1: 6 inches, 14 inches, 21 inches
Shelf 2: 10 inches, 15 inches, 24 inches
Shelf 3: 11 inches, 20 inches, 32 inches
Shelf 4: 8 inches, 20 inches, 24 inches

Which of the above shelf dimensions are not possible?

[removed] Shelf 2 and Shelf 4

[removed] Shelf 1 and Shelf 3

[removed] Shelf 1 and Shelf 2

[removed] Shelf 3 and Shelf 4



Question 37 (Multiple Choice Worth 4 points)

(10.04 HC) <object:standard:ma.912.g.3.4>

In a quadrilateral ABCD, the diagonals intersect at point T. Side AB is parallel and congruent to side DC. 

Based on the given conditions, which statement is presented first to show that segment DT is equal to segment TB?

[removed] Angle CDB and angle CBD are congruent.

[removed] Segment DT is congruent to segment CT.

[removed] Segment AT is congruent to Segment BT.

[removed] Angle CDB and angle ABD are congruent.



Question 38 (Multiple Choice Worth 4 points)

(3.01 MC) <object:standard:ma.912.g.4.7>
In a throw ball game, Ben, Ted, Mike and John are positioned at different points, as shown below. 

Three concentric circles are drawn with the 4 quadrants. Ben and Ted are shown as points standing in two adjacent quadrants on the line of the outermost circle.  Mike and John are shown as points standing in two remaining adjacent quadrants on the line of the middle circle.  Four segments are drawn, each joining the center to the four players. A segment joins Ben and Mike in the opposite quadrants, the included angle between the radii of the triangle formed between Ben and Mike is 100°. Another segment joins Ted and John in the remaining opposite quadrants, the included angle between the radii of the triangle formed by Ted and John is 120°. 

Which of the following statements is correct?

[removed] A longer pass will be required between Ted and John than Ben and Mike.

[removed] A shorter pass will be required between Ted and John than Ben and Mike.

[removed] A shorter pass will be required between Ted and John than Ted and Mike.

[removed] A longer pass will be required between Ben and John than Ben and Mike.



Question 39 (Multiple Choice Worth 4 points)

(3.04 LC) <object:standard:ma.912.g.4.5>
Look at the figure below. 
A triangle ABC is shown. A parallel line DF intersects AB in D and AC in F. Length of AC is 13, AF is 6, AD is x plus 9 and DB is 14 

What is the value of x?

[removed] 4

[removed] 3

[removed] 6

[removed] 5



Question 40 (Multiple Choice Worth 4 points)

(5.02 MC) <object:standard:ma.912.g.3.1>
Which statement about a kite and trapezoid is true?

[removed] A trapezoid is similar to a kite because both have diagonals which bisect each other at 90°.

[removed] Both are parallelograms because their opposite sides are congruent.

[removed] A trapezoid is different from a kite because it does not have two pairs of non parallel opposite sides.

[removed] Both are parallelograms because they have four sides and their diagonals are equal in length.



Question 41 (Multiple Choice Worth 4 points)

(07.04 MC) MA.912.G.7.5

A spherical fish bowl is half-filled with water. The center of the bowl is C, and the length of segment AB is 20 inches, as shown below. Use Twenty two over seven for pi.

A sphere with diameter 20 inches is drawn.

What is volume, in cubic inches, of water inside the fish bowl?

[removed] 2095.24

[removed] 3142

[removed] 2513.60

[removed] 4713



Question 42 (Fill-In-The-Blank Worth 4 points)

(01.04 MC)<object:standard:ma.912.g.1.3>

The figure below shows line AB parallel to line CD. Segment EF is parallel to segment GH. 

AB and CD are parallel lines. EF and GH are transversals which are parallel to each other. The measure of angle EFC is x plus 10.  The measure of angle HGB is 2 multiplied by x minus 40

What is the value of x?

Answer for Blank 1: [removed]



Question 43 (Multiple Choice Worth 4 points)

(5.04 MC) <object:standard:ma.912.g.3.3>
A quadrilateral EFGH has coordinates E (-1, -2), F (5, -2), G (5, -8) and H (-1, -8). Quadrilateral EFGH has

[removed] diagonals that are unequal

[removed] diagonals that do not bisect

[removed] all four sides equal

[removed] opposite sides unequal



Question 44 (Multiple Choice Worth 4 points)

(5.05 HC) <object:standard:ma.912.g.3.3>
The vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4). The vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). Which conclusion is true about the quadrilaterals?

[removed] The measure of their corresponding angles is equal.

[removed] The ratio of their corresponding angles is 1:2.

[removed] The ratio of their corresponding sides is 1:2

[removed] The size of the quadrilaterals is different but shape is same.



Question 45 (Fill-In-The-Blank Worth 4 points)

(6.05 MC) <object:standard:ma.912.g.2.3>

Tia photocopied the image of a design for a monorail track system. The figure below shows the design and its photocopy. 

Two irregular quadrilaterals ABCD and EFGH are drawn. EFGH is the photocopy of design ABCD. AB measures 17 meters, BC measures 14 meters. No dimensions on EFGH are shown. 

The ratio of DA : CD is 2 : 3. The total length of track on the design is 46 meters. What is the length, in meters, of side EH on the photocopied image?

Answer for Blank 1: [removed]



Question 46 (Multiple Choice Worth 4 points)

(2.05 MC) <object:standard:ma.912.g.4.2>
Look at the triangle KLM. O is the incenter and N is the circumcenter of the triangle. 

an obtuse triangle KLM is drawn. KO bisects angle MKL. LO bisects angle KLM. Incenter is at O. A point outside the triangle is labeled N and represents the circumcenter of the triangle 

Which statement is true?

[removed] The perpendicular from point N on KO bisects segment KO into two equal parts.

[removed] The perpendicular drawn from point N on segment ML will bisect ML.

[removed] Segment MN will bisect angle KOL.

[removed] Line MO is perpendicular to segment KL.



Question 47 (Fill-In-The-Blank Worth 4 points)

(3.02 LC) <object:standard:ma.912.g.4.4>
Look at the congruent triangles ABC and PQR. 

Two triangles ABC and PQR. Measure of angle BAC is equal to measure of angle PQR = 45°. Measure of angle ABC is equal to measure of angle RPQ. AB=7, AC=5, RQ=5 

What is the length of QP?

Answer for Blank 1: [removed]



Question 48 (Multiple Choice Worth 4 points)

(6.01 MC)<object:standard:ma.912.g.2.1>

The figure below shows two polygons. 

Two polygons labeled Polygon A and Polygon B. Both are quadrilaterals. Polygon A has opposite sides of equal length and the other pair of opposite sides significantly longer. Three interior angles are right angles. Polygon B has all only one pair of opposite sides of the same length and no angles shown. 

Gabrielle said that both are irregular convex polygons. Is Gabrielle correct?

[removed] Yes, all the angles are not of the same measure in both.

[removed] No, Polygon A is regular because all interior angles measure the same.

[removed] No, Polygon A is concave because it has two angles that measure greater than 180 degrees.

[removed] Yes, all the sides are not of the same length in both.



Question 49 (Multiple Choice Worth 4 points)

(02.04 MC)<object:standard:ma.912.g.4.2>

Look at the triangle PQR. 

An acute triangle PQR is drawn. PS is a segment from P which makes a right angle at S on RQ and QT is a segment drawn from Q to PR bisecting PR at T. A is the point of intersection of PS and QT

Which statement is true about line segments PS and QT?

[removed] Point A is the orthocenter of triangle PQR.

[removed] PS is the altitude and QT is the median of triangle PQR.

[removed] PS is the median and QT is the altitude of triangle PQR.

[removed] Point A is the centroid of triangle PQR.



Question 50 (Multiple Choice Worth 4 points)

(6.01 MC)<object:standard:ma.912.g.2.2>

The figure shows a pattern of a regular octagon and squares. 

A regular octagon with four squares on four of its sides is shown. An interior angle of the octagon is marked x 

Which of the following describes a method to find the measure of angle x?

[removed] The side of the octagon extends to form the diagonal of the square. The sum of x and 45° is 360°. x = 360°- 45°.

[removed] The interior angle of the octagon is 360° minus the interior angle of the square. x = 360° – 90°.

[removed] Extend the side of the octagon to get the diagonal of the square. The exterior angle of the octagon is 90° ÷ 2 = 45°. x = 180°- 45°.

[removed] The exterior angle of the octagon is the same as the interior angle of the square. x = 180°- 90°.



Question 51 (Multiple Choice Worth 4 points)

(6.02 MC) <object:standard:ma.912.g.2.4>

The coordinates of rectangle ABCD are A(-3, 6), B(-8, 6), C(-8, 2), D(-3, 2). What are the coordinates of the point of intersection of the diagonals of the rectangle after the rectangle is reflected across the y-axis?

[removed] (-5.5, -4)

[removed] (-5.5, -2)

[removed] (5.5, 4)

[removed] (2.5, 4)



Question 52 (Multiple Choice Worth 4 points)

(3.04 MC) <object:standard:ma.912.g.4.5>
Town 1 and Town 2 are situated 6 km apart on the bank of a river. The school and the church are 1km apart situated on the other bank of the river. The market is situated 5 km away from the school, as shown below. 

Two parallel lines represent the river. The school and church are 1 km apart on one side of the river and town 1 and town 2 are 6 km apart on the other side of the river. The market is on the same side of the river as the school and the church. The distance between the market and the school is 5 km. Straight lines join market and school and market and church. Straight lines join school and town 1 and church and town 2. 

How far is the school from Town 1?

[removed] 11 km

[removed] 25 km

[removed] 12 km

[removed] 30 km



Question 53 (Fill-In-The-Blank Worth 4 points)

(07.04 MC) <object:standard:ma.912.g.7.5>

A city park has an architectural pillar in the shape of a triangular pyramid. The shape of the base of the pillar is an equilateral triangle. The dimensions of the shape of the pillar are as shown below.

A triangular pyramid is shown. The shape of the base of the pyramid is an equilateral triangle having sides of length 2 feet. The lateral height is labeled as 14 ft. 

The park plans to repaint the lateral area of the pillar. The area of the pillar that will be repainted is _______________ ft2.

Answer for Blank 1: [removed]



Question 54 (Fill-In-The-Blank Worth 4 points)

(6.01 MC) <object:standard:ma.912.g.2.2>

Look at the table below. 

Regular Polygon

Number of Triangles the Polygon can be Divided Into

Sum of the Angle Measures of the Polygon





A square with a diagonal drawn


180° x 2 = 360°



a regular hexagon divided into 4 triangles. The vertex of each triangle is a vertex of the hexagon


180° x 4 = 720°



a regular octagon divided into 6 triangles. The vertex of each triangle is a vertex of the octagon


180° x 6 = 1080°

Based on the pattern in the table, what is the sum of the measures of the interior angles of a regular polygon with 18 sides?

Answer for Blank 1: [removed]



Question 55 (Multiple Choice Worth 4 points)

(09.02 MC) <object:standard:ma.912.g.8.4>

The figure below shows a parallelogram ABCD with diagonals AC and BD. 

The figure shows parallelogram ABCD with diagonals AC and BD.

If it is given that angle DAB is 60°, which statement will guarantee that the parallelogram is a rhombus?

[removed] Angle ABC is 120° and angle BCD is 60°.

[removed] Angle CAB is 30°.

[removed] Angle CAB is 30° and angle DBA is 30°.

[removed] Angle CAB is 30° and angle DBA is 60°.



Question 56 (Multiple Choice Worth 4 points)

(09.02 MC) <object:standard:ma.912.d.6.4>

Read the statements shown below. 

If a closed figure has three line segments joined end to end, it is a triangle. 
If all the three angles of a triangle are congruent, it is an equilateral triangle. 
Morgan constructed a triangle with all three sides congruent in the geometry class. 

Based on the given statements, which is a valid argument?

[removed] It cannot be concluded that Morgan drew an equilateral triangle.

[removed] It can be concluded that Morgan drew a closed figure having three congruent line segments joined end to end.

[removed] It cannot be concluded that Morgan drew a closed figure having three line segments joined end to end.

[removed] It can be concluded that Morgan drew a rectangle.



Question 57 (Multiple Choice Worth 4 points)

(02.01 LC)<object:standard:ma.912.g.4.1>

Isaac and Betty are describing two triangles.

Isaac says, ”My triangle has exactly two sides equal.”
Betty says, ”My triangle has all sides unequal.”

Which triangles did Isaac and Betty describe?

[removed] Isaac described an equilateral triangle, and Betty described a right triangle.

[removed] Isaac described an isosceles triangle, and Betty described a scalene triangle.

[removed] Isaac described a right triangle, and Betty described an equilateral triangle.

[removed] Isaac described a scalene triangle, and Betty described a right triangle.



Question 58 (Multiple Choice Worth 4 points)

(02.03 MC)<object:standard:ma.912.g.1.1>

Look at the points P and Q.

Points P (2, 4) and Q (-6, -4) are plotted on the coordinate axis.

M is the midpoint of the line segment joining points P and Q. At which point should M be plotted?

[removed] (-4, 0)

[removed] (6, -10)

[removed] (-1, -1)

[removed] (-2, 0)



Question 59 (Multiple Choice Worth 4 points)

(8.01, 8.04 HC) <object:standard:ma.912.g.6.5 ma.912.g.6.2=”” ma.912.g.6.4=””>

The figure below shows a circular prop with two triangles labeled ABC and AOC made on it. The center of the prop is labeled O. 

A circle is drawn with an inscribed triangle ABC. Angle ABC measures 45 degrees. O is the center of the circle. Triangle AOC has AC equal to 5 feet. 

What is the area of the cloth required to make the circular prop?

[removed] 23.60 ft2

[removed] 17.83 ft2

[removed] 39.27 ft2

[removed] 29.63 ft2


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