Triangle Similarity & Trig
Q1 (diagram): On the set of axes, AB is dilated by a scale factor of 5/2 centered at point P. Which statement is always true?
a) segment PA = segment AA'
b) segment AB || segment A'B'
c) AB = A'B'
d) (5/2) (A'B') = AB
Q1: b) segment AB || segment A'B'
Q2: The coordinates of the vertices of parallelogram CDEH are C(-5, 5), D(2, 5), E(-1, 1), and H(-8, -1). What are the coordinates of P, the point of intersection of diagonals CE and DH?
a) (-2, 3)
b) (-2, 2)
c) (-3, 2)
d) (-3, -2)
Q2: c) (-3, 2)
Q6: What are the coordinates of the center and the length of the radius of the circle whose equation is x2+y2=8x-6y+39?
a) center (-4, 3) and radius 64
b) center (4, -3) and radis 64
c) center (-4, 3) and radius 8
d) center (4, -3) and radius 8
Q6: d) center (4, -3) and radius 8
Q9 (diagram): Triangle ABC and RST are graphed on the axes. Which sequence of rigid motions will prove Triangle ABC = Triangle RST?
a) a line reflection over y=x
b) a rotation of 180˙ centered at (1, 0)
c) a line reflection over the x-axis followed by a translation of 6 units right
d) a line reflection over the x-axis followed by a line reflection over y=1
Q9: b) a rotation of 180˙ centered at (1, 0)
Q7 (diagram): In the diagram of parallelogram ABCD, segment AFGB, CF bisects Angle DCB,DG bisects Angle ADC, andCF and DG intersect at E. If Angle B = 75˙, then the measure of Angle EFA is
a) 142.5˙
b) 127.5˙
c) 52.5˙
d) 37.5˙
Q7: b) 127.5˙
Q18 (diagram): In the diagram, BC connects points B and C on the congruent sides of isosceles triangle ADE, such that Triangle ABC is isosceles with vertex Angle A. If AB=10, BD=5, and DE=12, what is the length of BC?
a) 6
b) 7
c) 8
d) 9
Q18: c) 8
Q8: What is an equation of a line that is perpendicular to the line whose equation is 2y + 3x = 1?
a) y = (2/3)x + (5/2)
b) y = (3/2)x + 2
c) y = (-2/3)x + 1
d) y = (-3/2)x + (1/2)
Q8: a) y = (2/3)x + (5/2)
Q12 (diagram): Circle O with a radius of 9 is drawn. The measure of central angle AOC is 120˙. What is the area of the shaded sector of circle O?
a) 6pi
b) 12pi
c) 27pi
d) 54pi
Q12: d) 54pi
Q5 (diagram): In the diagram of Triangle ACD, DB is a median to AC, and AB = DB. If Angle DAB = 32˙, what is Angle BDC?
a) 32˙
b) 52˙
c) 58˙
d) 64˙
Q5: 3) 58˙
Q16 (diagram): In the diagram of right triangle ABC, altitude CD intersects hypotenuse AB at D. Which equation is always true?
a) AD/CD = CD/BC
b) AD/CD = BD/CD
c) AC/CD = BC/CD
d) AD/AC = AC/BD
Q16: a) AD/AC = CD/BC
Q19 (diagram): In Triangle ABC, angle C is a right angle. Which statement must be true?
a) sin A = cos B
b) sin A = tan B
c) sin B = tan A
d) sin B = cos B
Q19: a) sin A = cos B
Q10: If the line represented by y = (-1/4)x - 2 is dilated by a scale factor of 4 centered at the origin, which statement about the image is true?
a) The slope is (-1/4) and the y-intercept is -8.
b) The slope is (-1/4) and the y-intercept is -2.
c) The slope is -1 and the y-intercept is -8.
d) The slope is -1 and the y-intercept is -2.
Q10: a) The slope is (-1/4) and the y intercept is -8.
Q22 (diagram): In the diagram, chords PQ and RS of circle O intersect at T.Which relationship must always be true?
a) RT=TQ
b) RT=TS
c) RT+TS = PT+TQ
d) RT*TS = PT*TQ
Q22: d) RT*TS = PR*TQ
Q4: If the altitudes of a triangle meet at one of the triangles vertices, then the triangle is a...
a) a right triangle
b) an acute triangle
c) an obtuse triangle
d) an equilateral triangle
Q4: a) a right triangle
Ms. Cheung life story (100):
What borough did Ms. Cheung grow up in?
Ms. Cheung life story (100):
Queens
a) 6.3
b) 7.0
c) 12.9
d) 13.6
Q24: a) 6.3
Q13: In quadrilateral QRST, diagonals QS and RT intersect at M. Which statement would always prove quadrilateral QRST is a parallelogram?
a) Angle TQR and Angle ARS are supplementary.
b) QM=SM and QT=RS
c) QR=TS and QT=RS
d) QR=TS and QT || RS
Q13: c) QR=TS and QT=RS
Q23 (diagram): A rhombus is graphed on the set of axes. Which transformation would carry the rhombus onto itself?
a) 180˙ rotation counterclockwise about the origin
b) reflection over the line y = (1/2)x + 1
c) reflection over the line y=0
d) reflection over the line x=0
Q23: d) reflection over the line x=0
Ms. Cheung life story (200):
Which borough did Ms. Cheung go to high school in?
Ms. Cheung life story (200):
The Bronx
Q15: Chelsea is sitting 8 feet from the foot of a tree. From where she is sitting, the angle of elevation of her line of sight to the top of the tree is 36˙. If her line of sight starts 1.5 feet above ground, how tall is the tree, to the nearest foot?
a) 8
2) 7
3) 6
4) 4
Q15: b) 7
Ms. Cheung life story (300):
Name 2/5 rides that Ms. Cheung went on yesterday at Six Flags.
Ms. Cheung life story (300):