Triangle Similarity & Trig
Quadrilaterals
Circles
Congruence: Rigid Motions & Triangles
CHALLENGE
200

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'

200

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)

200

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

200

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)

200

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˙

201

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

201

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)

201

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

201

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˙

Q53) 58˙

201

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

202

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

202

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.

202

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

202

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

202

Ms. Cheung life story (100):

What borough did Ms. Cheung grow up in?

Ms. Cheung life story (100):

Queens

203
Q24: A 15-foot ladder leans against a wall and makes an angle of 65˙ with the ground. What is the horizontal distance from the wall to the base of the ladder, to the nearest tenth of a foot?


a) 6.3

b) 7.0

c) 12.9

d) 13.6


Q24: a) 6.3

203

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

203

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

203

Ms. Cheung life story (200): 

Which borough did Ms. Cheung go to high school in?

Ms. Cheung life story (200): 

The Bronx

204

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

204

Ms. Cheung life story (300):

Name 2/5 rides that Ms. Cheung went on yesterday at Six Flags.

Ms. Cheung life story (300):


M
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