- Questions
MATH
Read the following statement:
Line segment GH is congruent to line segment IJ.
Which of the following is an equivalent statement?
GH over bar congruent to IJ overbar
GH over bar similar to IJ overbar
GH over bar equal to IJ overbar
GH over bar element of IJ overbar
Question 2(Multiple Choice Worth 1 points)
(02.06 LC)
The figure below shows two parallel lines cut by a transversal:
A pair of parallel lines is shown with arrowheads on each end. A transversal cuts through these two lines. An angle formed between the top parallel line and the transversal on the outer right side is marked 1. Another angle formed between the top parallel line, and the transversal on the inner right side is marked 2.
Which statement is true about ∠1 and ∠2?
∠1 and ∠2 are complementary, because they are a pair of adjacent angles.
∠1 and ∠2 are supplementary, because they are pair of adjacent angles.
∠1 and ∠2 are complementary, because they are a pair of corresponding angles.
∠1 and ∠2 are supplementary, because they are pair of corresponding angles.
Question 3(Multiple Choice Worth 1 points)
(02.01 MC)
Which translation will change figure ABCD to figure A'B'C'D'?
Polygon ABCD is drawn in the 4th quadrant of a 6 by 6 grid. Point A is at the ordered pair 4, negative 2, point B is at the ordered pair 6, negative 4, point C is at the ordered pair 2, negative 5, and point D is at the ordered pair 2, negative 3. Polygon A prime B prime C prime and D prime is drawn in the 2nd quadrant. Point A prime is at the ordered pair negative 4, 5, point B prime is at the ordered pair negative 2, 3, point C prime is at the ordered pair negative 6, 2, and point D prime is at the ordered pair negative 6, 4.
7 units left and 8 units up
8 units left and 7 units up
7 units left and 5 units up
5 units left and 7 units up
Question 4(Multiple Choice Worth 1 points)
(02.07 LC)
The figure shows the two similar triangles:
Two triangles are shown. The sides of the triangle on the left are marked 6, 8, 4. The sides of the triangle on the right are marked as 3, 4 and 2. For the triangle on the left, the angle between sides marked 8 and 6 is labeled as p, marked with a single arc, and the angle between the sides marked 8 and 4 is labeled as q, marked with a double arc. The angle is marked with a triple arc. For the triangle on the right, the angle between sides marked 2 and 4 is labeled as s, marked with a double arc, and the angle between the sides marked 4 and 3 is labeled as r, marked with a single arc. The angle between the sides 2 and 3 is labeled as t marked with a triple, and it is also the angle on the top vertex of this triangle.
Which two sets of angles are corresponding angles?
∠p and ∠s; ∠q and ∠r
∠p and ∠t; ∠q and ∠s
∠p and ∠t; ∠q and ∠r
∠p and ∠r; ∠q and ∠s
Question 5(Multiple Choice Worth 1 points)
(02.06 MC)
A pair of parallel lines is cut by a transversal:
A pair of parallel lines is cut by a transversal. The interior angle made on the left by the intersection of the upper parallel line and the transversal is divided into 2 parts by a slanting line. One part of this angle is labeled as x and the other part is labeled as 30 degrees. The interior angle made on the right by the intersection of the lower parallel line and the transversal is labeled as 70 degrees.
What is the measure of angle x?
30 degrees
40 degrees
70 degrees
110 degrees
Question 6(Multiple Choice Worth 1 points)
(02.03 MC)
The figure shows two triangles on a coordinate grid:
A coordinate grid is shown from positive 6 to negative 6 on the x axis and from positive 6 to negative 6 on the y axis. A triangle ABC is shown with vertex A on ordered pair 4, negative 2, vertex B on ordered pair 3, negative 2 and vertex C on ordered pair 3, negative 5. Another triangle A prime B prime C prime is shown with vertex A prime on ordered pair 1, 2, vertex B prime on ordered pair 2, 2 and vertex C prime on ordered pair 2, 5.
What set of transformations is performed on triangle ABC to form triangle A'B'C'?
A 180 degree counterclockwise rotation about the origin followed by a translation 5 units up
A 270 degree counterclockwise rotation about the origin followed by a translation 5 units up
A translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin
A translation 5 units to the left followed by a 270 degree counterclockwise rotation about the origin
Question 7(Multiple Choice Worth 1 points)
(02.05 MC)
The figure shows two similar triangles on a coordinate grid:
A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle ABC is shown with vertex A on ordered pair 1, 2, vertex B on ordered pair 0, 0 and vertex C on ordered pair 3, negative 1. A triangle A prime B prime C prime is also shown with vertex A prime on ordered pair negative 2, 4, vertex B prime on ordered pair 0, 0 and vertex C prime on ordered pair negative 6, negative 2.
Which set of transformations have been performed on triangle ABC to form triangle A'B'C'?
Dilation by a scale factor of 2 followed by reflection about the x-axis
Dilation by a scale factor of 4 followed by reflection about the x-axis
Dilation by a scale factor of 2 followed by reflection about the y-axis
Dilation by a scale factor of 4 followed by reflection about the y-axis
Question 8(Multiple Choice Worth 1 points)
(02.03 MC)
The figure ABCD is transformed to A'B'C'D', as shown:
A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes. A polygon ABCD has A at ordered pair 2, negative 2, B at ordered pair 4, negative 1, C at ordered pair 3, negative 4, D at ordered pair 2, negative 4. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 2, 3, B prime at ordered pair negative 4, 4, C prime at ordered pair negative 3, 1, D prime at ordered pair negative 2, 1.
Which of the following sequence of transformations is used to obtain figure A'B'C'D' from ABCD?
Reflection about the x-axis followed by translation down by 5 units
Counterclockwise rotation by a 180 degree about the origin followed by translation down by 5 units
Reflection about the y-axis followed by translation up by 5 units
Counterclockwise rotation by a 180 degree about the origin followed by translation up by 5 units
Question 9(Multiple Choice Worth 1 points)
(02.07 MC)
What is the measure of ∠CED?
There are two triangles labeled ABC and DCE with a common vertex C. In triangle ABC, angle BAC is labeled as x, angle ABC is labeled as 75 degrees. In triangle DCE, angle CDE is labeled as 75 degrees.
x over 2, because Triangle ABC is congruent to triangle EDC
x + 75 degrees, because Triangle ABC is similar to triangle EDC
105 degrees − x, because Triangle ABC is congruent to triangle EDC
x, because Triangle ABC is similar to triangle EDC
Question 10(Multiple Choice Worth 1 points)
(02.05 LC)
The figure shows three quadrilaterals on a coordinate grid:
A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. An image of a rectangle labeled U is shown on ordered pair 1, 1 and 3, 1 and 3, 2 and 1, 2. Another image of a rectangle labeled V is shown on ordered pair 2, 2 and 6, 2 and 6, 4 and 2, 4. Another image of a rectangle labeled W is shown on ordered pair negative 1, 1 and negative 1, 2, and negative 3 , 2 and negative 3, 1.
Which of the following statements is true about the three quadrilaterals?
U and W are similar but not congruent.
U and V are similar and also congruent.
U and V are similar but not congruent.
V and W are similar and also congruent.
Question 11(Multiple Choice Worth 1 points)
(02.06 MC)
The figure shows two parallel lines AB and CD cut by transversals EF and GH. Angle EKD measures 90 degrees.
AB is parallel to CD. EF and GH are transversals that cut CD at the same point. The angle between the transversals at the point where they meet CD is 50 degrees. GH makes an angle x with AB. EF is perpendicular to AB and CD.
What is the measure of angle x?
35 degrees
40 degrees
45 degrees
50 degrees
Question 12(Multiple Choice Worth 1 points)
(02.01 LC)
Figure PQRS is translated down by 3 units:
A coordinate grid is shown with scale from negative 6 to 0 to 6 on both x- and y-axis at increments of 1. A polygon PQRS is shown in the first quadrant. Point P is the ordered pair 3, 4, point Q is the ordered pair 5,1, point R is the ordered pair 1,1, and point S is the ordered pair 1,4.
Which of the following best describes the sides of the transformed figure P'Q'R'S'?
Side P prime S prime is parallel to side P prime Q prime
Side P prime Q prime is parallel to side Q prime R prime
Side P prime S prime is parallel to side Q prime R prime
Side S prime R prime is parallel to side P prime S prime
Question 13(Multiple Choice Worth 1 points)
(02.02 MC)
Which transformation changes triangle ABC to triangle A'B'C'?
A coordinate grid is labeled from negative 6 to 0 to 6 on both axes. Triangle ABC is drawn in the first quadrant. Point A is the ordered pair 1, 4, point B is the ordered pair 4,1, point C is the ordered pair 3, 5. Triangle A prime, B prime, C prime is drawn in the fourth quadrant. Point A prime is the ordered pair 4, negative 1, point B prime is the ordered pair 1, negative 4, point C prime is the ordered pair 5, negative 3.
Reflection about the y-axis followed by translation up by 2 units
Rotation 270 degrees counterclockwise about the origin
Reflection about the x-axis followed by translation left by 5 units
Rotation 180 degrees counterclockwise about the origin
Question 14(Multiple Choice Worth 1 points)
(02.07 HC)
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
A triangle ABC is shown. The base of triangle extends into a straight line. The angle formed between this straight line and the edge of triangle is marked as d. The angle adjacent to w is marked as c, and the other two angles inside the triangle are marked as a and b.
Step 1: m∠a + m∠b + m∠c = 90 degrees (complementary angles)
Step 2: m∠d + m∠c = 180 degrees (supplementary angles)
Step 3: Therefore, m∠a + m∠b + m∠c = m∠d + m∠c
Step 4: So, m∠a + m∠b = m∠d
In which step did the student first make a mistake and how can it be corrected?
Step 1; it should be m∠a + m∠b + m∠c = 180 degrees (corresponding angles)
Step 1; it should be m∠a + m∠b + m∠c = 180 degrees (sum of angles of a triangle)
Step 2; it should be m∠d − m∠c = 90 degrees (alternate interior angles)
Step 2; it should be m∠d − m∠c = 90 degrees (adjacent angles)
Question 15(Multiple Choice Worth 1 points)
(02.05 MC)
Which statement is true about figures ABCD and A'B'C'D'?
A polygon ABCD has A at ordered pair negative 2, 3, B at negative 4, 2, C at negative 2 and 1, D at negative 1 and 2. A polygon A prime B prime C prime D prime has A prime at ordered pair 0,negative 2, B prime at ordered pair 1, negative 4, C prime at ordered pair 2, negative 2 and D prime at ordered pair 1, negative 1.
They are similar, because A'B'C'D' is obtained by rotating ABCD counterclockwise by 90 degrees about the origin and then translated 3 units right.
They are congruent, because A'B'C'D' is obtained by translating ABCD up by 2 units and then reflecting it about the y-axis.
They are congruent, because A'B'C'D' is obtained by translating ABCD 2 units right and then reflecting it about the x-axis.
They are similar, because A'B'C'D' is obtained by rotating ABCD counterclockwise by 90 degrees about the origin and then translating it 3 units left.
Question 16(Multiple Choice Worth 1 points)
(02.02 MC)
Line segment CD is shown on the coordinate grid:
A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A line segment CD is shown with C as ordered pair 1, negative 3 and D as ordered pair 5, negative 3.
The line segment is rotated by 270 degrees counterclockwise about the origin to form C'D'. Which statement describes C'D'?
C'D' is 4 units long.
C'D' is 8 units long.
C'D' is parallel to CD.
C'D' is half the length of CD.
Question 17(Multiple Choice Worth 1 points)
(02.01 LC)
Line segment AB has a length of 2 units. It is translated 6 units to the right on a coordinate plane to obtain line segment A'B'. What is the length of A'B'?
2 units
4 units
6 units
8 units
Question 18(Multiple Choice Worth 1 points)
(02.05 LC)
Which sequence of transformations creates a similar but not congruent triangle?
Rotation and translation
Dilation and reflection
Reflection and rotation
Translation and reflection
Question 19(Multiple Choice Worth 1 points)
(02.02 LC)
A shape is shown on the graph:
A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. A triangle is shown on ordered pair negative 6, negative 2 and negative 6, negative 4 and negative 2, negative 4.
Which of the following is a reflection of the shape?
A coordinate grid is shown from positive 8 to negative 8 on the axis and from positive 8 to negative 8 on the y-axis. A triangle is shown on ordered pair 2, negative 2 and 4, negative 2 and 2, negative 6.
A coordinate grid is shown from positive 8 to negative 8 on the axis and from positive 8 to negative 8 on the y-axis. A triangle is shown on ordered pair negative 2, 2 and negative 4, 2, and negative 4, 6.
A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. A triangle is shown on ordered pair 6, negative 2 and 6, negative 4 and 2, negative 4.
A coordinate grid is shown from positive 8 to negative 8 on the axis and from positive 8 to negative 8 on the y-axis. A triangle is shown on ordered pair negative 6, 2 and negative 2, 2, and negative 6, 4.