2D Geometry Questions and Answers

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A point in the figure shaded region A l W 4 17 m 8 m

12 Find the value of x and y Hint Find x first Then use x to findy x y 5 X 5 4

10 Parallelogram HIJK 1J HK 18 4 JK d x x HI P A 0 6 H K 4 B B X

In 3 11 Find the indicated information P is perimeter A is area Round answers to the nearest tenths Drawings are not to scale Don t Forget Units 3 11 m 4 X 21 ft 8 1 m P 6 4 m x P A 20 ft

In 1 2 Use Pythagorean s Theorem to find the value of x in each right triangle Round answers to the nearest tenths Drawings are not to scale Don t Forget Units 1 18 in 5 in x X 2 8 in A 36 in 11 in x

11 2 In the diagram below DE BC ANI DE and BC DB Write down the values of 11 21 AM MN 11 2 2 DE BC 11 2 3 area AADE area LABC M E 2 4 3

14 In general a cardboard fan with a greater area does a better job of moving air and cooling you The fan shown is a sector of a cardboard circle Another fan has a radius of 6 centimeters and an intercepted arc of 150 Which fan does a better job of cooling you 120 9 cm

5 Please give exact answers 5 If rectangle ABCD has an area of 64 3 m find its dimensions AC is a diagonal and the measure LBAC is 30 short side length Jonger side lenath

Find the area of the regular polygon 8 9 a hexagon with an apothem of 9 centimeters a nonagon 9 gon with a radius of 1 meter

Find the area of the composite figure 1 111 6 yd 8 yd 12 yd 2 13 mm T 15 mm 17 mm 8 mm 3 9 cm 2 8 cm 5 2 cm 4 8 cm

3 B A C D FL

Determine whether each pair of tr 13 T W

d Name the postulate if possible that makes the triangles congruent A N B SAS AAS ASA Not Possible M C

8 6 7 km Sm 3 km 7 9 cm 40 cm 9 6 ft J

16 B F

Jeff is at the position marked X and wants to find the height of the tower shown Viewing from the ground he positions himself so that the top of the flagpole is directly in his line of sight to the tower The flagpole is known to be 18 feet tall Jeff is 20 feet from the flagpole and the flagpole is 40 feet from the tower How tall is the tower Both the flagpole and tower are assumed to be perpendicular to the ground

Jeff is at the position marked X and wants to find the height of the tower shown Viewing from the ground he positions himself so that the top of the flagpole is directly in his line of sight to the tower The flagpole is known to be 18 feet tall Jeff is 20 feet from the flagpole and the flagpole is 40 feet from the tower How tall is the tower Both the flagpole and tower are assumed to be perpendicular to the ground

AB BC CD DE EA P A d x x2 y y2 A B E D

P X A 9 19 7 cm 12 cm x I P X 8 cm A 6 cm

What is the area of a regular pentagon with a side of 12 in Round the answer to the nearest tenth 1 point 495 5 in 2 O 311 8 in 2 247 7 in 2 124 7 in 2

What is the circumference of the given circle in terms of 15 in 1 point O 30 in 45 in O 15 in 225 in

Given the regular polygon what is the measure of each numbered angle IN 1 point Oma1 12 mx2 72 Omx1 12 mx2 144 Oma1 36 m2 72 Oma1 36 m 2 144

What is the area of the given circle in terms of 6 6 m 1 point O 16 2 m O 10 89 m O 21 78 m 43 56 m2

3 As graphed on the set of axes below AA B C is the image of AABC after a sequence of transformations Is AA B C congruent to AABC Use the properties of rigid motion to explain your answer Trans for mation Direction Distanco

9 cos 240 1

7 tan 240

3 sin 300 14 cos 6

8 2 d x x2 2 AB BC 8 6 4 2 0 CD 2 B C DE 4 A D EF H E 6 FG 8 GH G F AH P A

Find the measure of the arc or central angle indicated Assume that lines which appear to be diameters are actual diameters Do not include units in your answer degrees degree symbols etc FR 60

Find the area of each Round to the nearest tenth Do not include units in your answer ie ft in km etc triangle FR 3 m 5 9 m

5 Extended Euclid algorithm Does the multiplicative inverse of 59 in Z61 exist If so find it using the extended Euclid algorithm I it does not exist state why Show all your steps

for the measure of arc ABC if BD is a diameter the measure of arc DC is 60 degrees and angle DMA is 98 degrees B A M D C

What is the measure of XY N 55 Y

4 Dana Bill and Rodrigo are given the following information about ATEA m T 71 TA 8 mZE 35 They are asked to determine the number of triangles that can be formed using these conditions and give a reason for their answer Dana says that two triangles are possible because ATEA is an acute triangle Bill says that only one triangle is possible because whenever the measures of two angles and a non included side are given AAS exactly one triangle is possible Rodrigo says that only one triangle is possible because the length of the fixed leg is less than the length of the swinging leg Which of these students is correct Explain

6 7 19 7 cm P 8 m A 12 cm 6 cm X P x 8 cm A

3 Pre image Quadrilateral HIJK H 2 2 I 2 2 J 2 2 K 2 2 Step 1 Rotate the figure 180 H I J K Step 2 Translate the figure according to x y x 2 y 2 H I I K Step 3 Reflect the figure over the line y x H I J K 3 4

1 P A x then find the Perimeter and the Area of each triangle Round to nearest tenths Drawings are not to scale x 15 in 12 in 2 6 5 cm x 2 8 cm P A

In 3 6 Find the value of each variable drawings are not to scale 3 x 4 x y N 115 99 148 112 176 1329 125 8 49 55 12 20

In 16 Identify all of the terms from the following list that apply to the figure quadrilateral parallelogram rectangle square trapezoid rhombus kite 16 I

15 Kite 1 35 2 34 mzl mz2 12 mz3 mZ4

8 Find the indicated information for the given Kite 3x 5 17 Find x Find y 3y 9

10 Find the indicated information for the given Rhombus EFGH E F GF 30 D Find GD ED 5x 8 EH 34 Find DF Find x H

9 Find the indicated information for the given Isosceles Trapezoid A B D C AC 7x 9 BD 4x 15 Find x Find AC

2 Pigeonhole principle Prove that if seven distinct numbers are selected from 2 3 4 12 then some two of these numbers will add up to 14 you can assume that the 7 can be picked up more than once Identify the pigeons and the holes Then using the Pigeonhole Principle prove that the statement is true

9 w x y 142 65 Z 10 x 152 140 135 76 205 889

In 12 17 Find the indicated information for each quadrilateral 12 Parallelogram ABCD B 312 5x 8 y 61 18 D 13 Kite LMNP 3y 6 L Sy 9 X M N 9x 15 12x 3

parallelogram rectangle square trapezoid rhombus kite 26 Identify all of the terms from the following list that apply to each figure quadrilateral 24 H 25 26 H H

16 Rectangle WXYZ W Y Z X WZ 10x 7 XY 6x 19 x 17 Square DEFG D 8x y E x 10x 2x 24 y F G 7x 9

4 Find TQ R 2x 5 14 2x 1 2 P T 18 S S