2D Geometry Questions and Answers

Find the measure of angle ZAGE in the figure below Enter only the A C 51 D The solution G F E B

A particle is at the point 3 5 at time 0 and a the point 7 2 at time 5 Plot the parametric equation that models this scenario

Identify the set of perpendicular A O E F B OAB LCD CD LEF AB L FE AB LEF

Does ABC appear to be the same size and shape as XYZ Explain A 5 C 13 O Y B 13 Z O A Yes AABC maps onto AXYZ with a translation and a rotation 5 B Yes AABC maps onto AXYZ with a translation and a reflection D No the triangles are different sizes C Yes AABC maps onto AXYZ with a rotation and a reflection

In square QUAD shown AD 6x ft and DQ 3x 3 ft a Determine the perimeter of the square b If mLBAU 5y determine the value of y D A B U

Use the figure shown b OB 22 62 OC 67 38 D 5 22 60 D D is the midpoint of AB and mZACB 134 76 What is m ZA OA 45 24 a B

WXYZ is a square If WT 6 find each measure ZX XY m WTZ perimeter of WXYZ T

Find xin Trapezoid PQRSi S P 51 X 28x 11 Q

EFGH is a rhombus with FH 24 and GE 10 Find the perimeter of EFGH Perimeter H

WXYZ is a rectangle Find each angle measure given m 1 30 7 6 8 S 1 4 2 M 1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10

1 1 point Look at the following graph below F H D K choose your answer 55 L C Given ZIKL 55 what postulate would prove ZKLJ 125 D B J E A 1 point Given the following graph and ZCXD 40 what must be the m BXC in degrees G

What is mZCBD B 60 80 mZCBD 25 C I

Provide the reasons for each statement in the proof Given AB DE Prove AD BE A B Statement AB DE AB BD DE BD AB BD AD AD BE C D Reason Given DE BD BE

riangle A B C a What transformation took place to get from triangle ABC to triangle A B C Be specific 2 points a b b What transformation took place to get from triangle A B C to triangle A B C Be specific 2 points B 9 8 7 6 5 B A 9 8 7 6 5 0 2 1 3 2 1 V A 1 2 3 4 5 Y 6 7 8 9 0 A B 2 3456

9 A graphic artist created a design for a flower using four congruent hexagons as shown Given BP 1 MK m2MYF m2FHB m2WMC m2WPT mzGXR 50 m2DNK 3x 18 and mzWBR 5x 8 The sum of the angles in WKNDSP is 720 Find each Show your work a m TLC F L Y C HR M W ay T B P S Work K G N

If one base angle of an isosceles trapezoid measures 42 what is the measure of the other base angle O 138 O 52 O 42 O 148

How many lines of symmetry can be drawn for this shape 05 04 6 07

Which diagram shows a reflection in the y axis 00 O 0 M A ANSE 0 y 1 1220 x X x None of the other answers are correct

Which transformation will create an image of MNOP that coincides with the original figure N 0 A reflection across the diagonal MO A 180 clockwise rotation about point Q O A reflection across the side MN A 90 counterclockwise rotation about point Q O None of the other answers are correct

A figure is dilated by a scale factor of 3 If the origin is the center of dilation what is the image of a vertex located at 3 4 0 1 1 1 O 3 12 9 4 9 12

In the diagram line d cuts three lines to form the angles shown below a 105 85 b Which two lines are parallel a and c Ob and c a and b no lines are parallel C 95

In the figure below what is the measurement of ZJLK K 14 72 70 78 100 M J 3x 30 2x L

4 Given m n find the value of x Type your answer 32 I I m 1 point What is the slope of a line that is perpendicular to the equation 3x 2y 12 23 32 8x 9 72 81

Which is the image of 4 7 rotated 180 degrees about the origin O 4 7 0 7 4 O 4 7 0 7 4 None of the other answers are correct

Trig Function 49 X 231 S Sin 45 25

In the triangle below with right angle ZW suppose that mZV 2x 19 and m ZX 3x 31 Find the degree measure of each angle in the triangle V 2x 19 3x 31 m4V mZW mZX 0 0 C

3 4 03 Review Graph the segment with endpoints C 1 5 and D 4 2 What are the coordinates of C and D under the transformation R 90 Pre Image Coordinates Pre Image Quadrant Image Quadrant Image Coordinates

6 In parallelogram ABCD DP 2y DB 3y 6 AP 3x 3 and CP 4x 2 a Determine the length of AC b Determine the length of PB A D P B

vertical or horizontal directions section 2 5 A graph of f x is shown below a Graph f x 1 b Graph f x 2 c Graph f x d Graph f x e Graph 2f x f Graph f 2x X x

2 Given Circle O Construct A regular octagon inscribed in circle O

In the graph below pentagon R S TU V is the image of RSTUV after a dilation R V scale factor 10 9 8 7 6 5 4 3 2 1 9 8 7 42 center of the dilation U 99 6 5 4 32 A TNP451 1 3 5 S 2 3 4 5 6 7 8 9 10 R S V 6 7 8 9 10 What are the scale factor and center of the dilation Simplify your answers and write them as fractions or whole numbers T S

47 Which of the following statements must be true Select all that apply 3y 4 D E G 5y 10 F A EG bisects ZDEF BADEF is isosceles EG is the perpendicular bisector of DF Dm DEG 25 L Q M m 7 48 What is LN P O 50which statement about the figure MUST be true Select all that apply A n 7 B QS 21 CSR 27 QR 54 A angle Which of the following describes MO Select all that apply median N 2m bisector B perpendicular altitude bisector 6n 3 S 4n 11 R

T W Z X U S V Y If TV and WY are parallel lines and m WXU 117 what is mZYXZ

Look at this diagram K N J L O O Q M P If KM and NP are parallel lines and mZKLO 116 7 what is m NOQ

Look at this diagram F I E Submit L H K If FH and IK are parallel lines and mZFGJ 114 what is m

B 6x 1 D A E B A 92 To show that AADB ACBD by AAS what must be the value of x 48 48 32 What is m BAC D 33 What is m CDE C 4x 25

4 a What is the value of x in the figure 21 54 57 23 The statement Angle 2 is congruent to angle 4 is justified by the 24 If mz1 equals 4x 2 and mz2 equals 110 what is the value of x A 14 15 16 17 maps the Items 6 7 What rigid motion solid line figure onto the dotted line figure 26 27 3344 22 104 49 What is the value of x x 35 3x 1 28 Which words have horizontal reflection symmetry A BOO B PIP CRADAR D EXCEED

statement All numbers that are divisible by 2 are divisible by 4 A O 28 B 12 D42 For the conjecture Write the converse and determin if it is true 15 A polygon with four congruent sides is a square 16 If a polygon is a triangle then it has 3 sides 17 If a quadrilateral is a rectangle then it has two pairs of parallel sides 18 In the figure shown what is the value of x x 17 6x 10 4x 34 46 51 38 What is the value of y 20 What is the value of x

S P 2 1 4 3 2 1 0 1 2 3 4 5 Q 2 3 S R 4

Which statement accurately explains whether a reflection over the y axis and a 270 counterclockwise rotation would map figure ACB onto itself W 2 0 A 2 3 Yes A C B is located at A 1 1 C 4 3 and B 1 5 Yes A C B is located at A 1 1 C 3 4 and B 5 1 ONo A C B is located at A 1 1 C 4 3 and B 1 5 No A C B is located at A 1 1 C 3 4 and B 5 1 5 B

Rectangle STUV is shown on a coordinate plane S V 3 9 3 4 T 9 8 7 6 5 4 3 2 1 2 4 U 2 9 8 7 6 10 5 4 3 2 1 2 3 4 5 6 7 8 9 1 2 If rectangle STUV is translated using the rule x y x 2 y 4 and then rotated 90 counterclockwise what is the location of S 2 3 4 5 67 8 9

Find an equation for the line below 2 9 8

A cone shaped container is oriented with its circular base on the top and its apex at the bottom It has a radius of 12 inches and a height of 8 inches The cone starts filling up with water What fraction of the volume of the cone is filled when the water reaches a height of 2 inches

For each of the following functions sketch the graph for 37 x 37 and calculate the Fourier series Each is 2 periodic f x if x x if x 0 0 x T g x if x 0 2x if 0 x T

3 SAT Question Find the value of x and y below 4 be Jo 4 x 2r

5 In the figure below line m is parallel to line n If m 3 degrees and mz5 30x 35 degrees a Solve for x 2 point b Find the angle measure of all eight angles below 4 point X m 1 m 2 m 3 m 4 m 5 m 6 m 7 m 8 1 2 3 4 5 6 7 8 m 12x 5

6 Complete the partial proof below Given AC 1 BD and AC bisects BD Prove AD AB A

4 1 point Find the perimeter of the following trapezoid if length a 27 m length b 33 m sides 12 m and length h 10 m h 84 m 45 m 324 m 33 m b

1 point Find the area of the following trapezoid if length a 27 m length b 33 m sides 12 m and length h 10 m a 0 h 720 m 2 300 m 2 360 m 2 600 m 2

19 1 point We started with a sheet of Aluminum 2 meters by 2 5 meters and 50 cm from the edges in one corner we cut a 30 cm diameter circular hole What is the remaining area of Aluminum 25 m 2 49 293 5 cm 2 701 86 cm 2 5m 2