Multiple-Choice Exercise From the New York State Education Department. Regents High School Examination. Internet. Available from http://www.nysedregents.org; accessed January 22, 2012.; All rights reserved. No commercial, for-profit use of this material is allowed. E-mail comments and questions to Tami Maloney.
Choose the correct answer for each question.
37
58
74
118
In △ABC, m∠A = x, m∠B = 2x + 2, and m∠C = 3x + 4. What is the value of x?
29
31
59
61
Which expression best describes the transformation shown in the diagram below?
same orientation; reflection
opposite orientation; reflection
same orientation; translation
opposite orientation; translation
Based on the construction below, which statement must be true?
In the diagram below, △ABC is inscribed in circle P. The distances from the center of circle P to each side of the triangle are shown.
Which statement about the sides of the triangle is true?
AB > AC > BC
AB < AC and AC > BC
AC > AB > BC
AC = AB and AB > BC
Which transformation is not always an isometry?
rotation
dilation
reflection
translation
20
9
8
6
Which geometric principle is used to justify the construction below?
A line perpendicular to one of two parallel lines is perpendicular to the other.
Two lines are perpendicular if they intersect to form congruent adjacent angles.
When two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel.
When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel.
Which equation represents the circle whose center is (−2,3) and whose radius is 5?
(x − 2)2 + (y + 3)2 = 5
(x + 2)2 + (y − 3)2 = 5
(x + 2)2 + (y − 3)2 = 25
(x − 2)2 + (y + 3)2 = 25
Towns A and B are 16 miles apart. How many points are 10 miles from town A and 12 miles from town B ?
1
2
3
0
Lines j and k intersect at point P. Line m is drawn so that it is perpendicular to lines j and k at point P. Which statement is correct?
Lines j and k are in perpendicular planes.
Line m is in the same plane as lines j and k.
Line m is parallel to the plane containing lines j and k.
Line m is perpendicular to the plane containing lines j and k.
In the diagram below of parallelogram STUV, SV = x + 3, VU = 2x − 1, and TU = 4x − 3.
5
2
7
4
Which equation represents a line parallel to the line whose equation is 2y − 5x = 10?
5y − 2x = 25
5y + 2x = 10
4y − 10x = 12
2y + 10x = 8
What is the degree measure of ∠CEA?
87
61
43.5
26
What is the distance between the points (−3,2) and (1,0)?
What is an equation of the line that contains the point (3,−1) and is perpendicular to the line whose equation is y = −3x + 2?
Which technique can be used to prove △PST ∼ △RQT?
SAS
SSS
ASA
AA
The equation of a circle is (x − 2)2 + (y + 4)2 = 4. Which diagram is the graph of the circle?
If m∠BCD = 6x + 2, m∠BAC = 3x + 15, and m∠ABC = 2x − 1, what is the value of x?
The pentagon in the diagram below is formed by five rays.
What is the degree measure of angle x?
72
96
108
112
Through a given point, P, on a plane, how many lines can be drawn that are perpendicular to that plane?
1
2
more than 2
none
What is the slope of a line that is perpendicular to the line whose equation is 3x + 4y = 12?
What is the image of point A(4,2) after the composition of transformations defined by R90° ∘ ry = x?
(−4,2)
(4,−2)
(−4,−2)
(2,−4)
Which expression represents the volume, in cubic centimeters, of the cylinder represented in the diagram below?
What is the inverse of the statement “If two triangles are not similar, their corresponding angles are not congruent”?
If two triangles are similar, their corresponding angles are not congruent.
If corresponding angles of two triangles are not congruent, the triangles are not similar.
If two triangles are similar, their corresponding angles are congruent.
If corresponding angles of two triangles are congruent, the triangles are similar.
