2D Geometry Questions and Answers

2 c C 46 1 8x B

T 5x 10 11x 2 U 58 S

Multiple Response Which coordinates can be used to describe the point on the grid to the right Check all that apply 5 2 5 117 5 2 5 37 76 25 5 77 5 37 5x T 7x 2T 3 4x 12 K 0 16 1 lt

Write the equation of the conic section shown below 10 9 8 7 6 5 4 3 2 1 focus 10 9 8 9 7 5 4 32 y 2 H 5 6 7 B 8 cl 3 4 5 9 7 00 8 9 10 X

10 8 pts Consider the triangle below not drawn to scale with a 26 cm b 12 cm and Y 20 Use the Law of Sines to find all possible values of c X and Z Show all work that leads up to your answer Round your final answers to one decimal place Include units in your answers b

For each of the following quadrilaterals select all the properties that must be true a Parallelogram b Square c Trapezoid All sides congruent Four right angles Only one pair of parallel sides Two pairs of parallel sides

AABC is shown on the coor late plane A After rotating AABC 180 about the origin and then reflecting it over the x axis what are the coordinates of AA B C A 2 6 B 5 4 C 2 1 A 6 2 B 4 5 C 1 2 A 2 6 B 4 5 C 2 1 A 6 2 B 4 5 C 1 2 Which of the following is NOT a correct name for the marked yellow angle E A B C D B A B C 22 ZE ZBEC

The radius of a circle is 6 ft Answer the parts below Make sure that you use the correct units in your answers If necessary refer to the list of geometry formulas a Find the exact circumference and area of the circle Write your answers in terms of Exact circumference Exact area 0 b Approximate the circumference and area of the circle To do the approximations use the button on the ALEKS calculator and round your answers to the nearest hundredth Approximate circumference Approximate area 00 ft X B ft 6 ft ft

The radius of a cylindrical water tank is 6 ft and its height is 16 ft Answer the parts below Make sure that you use the correct units in your answers If necessary refer to the list of geometry formulas a Find the exact volume of the tank Write your answer in terms of Exact volume 6 ft Approximate volume 16 ft b Using the ALEKS calculator approximate the volume of the tank To do the approximation use your answer to part a and the button on the calculator Round your answer to the nearest hundredth 00 ft X

A training field is formed by joining a rectangle and two semicircles as shown below The rectangle is 86 m long and 64 m wide What is the length of a training track running around the field Do not round any intermediate computations Round your final answer to the nearest hundredth and be sure to include the correct unit If necessary refer to the list of geometry formulas 86 m 64 m 0 m X m m G Esp

PORES Find the measure of each angle m2WXY 9 4b 6 mZXYW 4b 8 abel optional n

In circle A shown DF 6 cm EF 5 cm and BD 20 cm D E C F A What is the length of CF A 16 8 cm O B 28 EX

2 Determine the value of x Lines that appear to be tangent are tangent a b X 7 cm O 5 cm 6 cm 8 cm X 0 X 4 cm 6 cm c 12 cm 10 cm X X

8 A tree growing perpendicular to the ground casts a shadow that is 45 feet long If the angle of elevation from the end of the shadow to the top the tree is 32 what is the approximate height of the tree A 53 ft B 72 ft C 24 ft D 28 ft

30 students return to the classroom after playing outside at recess Over the course of the next hour each person produces 800 BTUS British Thermal Units of heat The room is 20 feet by 20 feet by 12 feet How many BTUs per cu foot were produced 5 0 BTU per ft 0 16 BTU per ft 15 3 BTU per ft 51 BTU per ft

an altitude of 1200 Ft The angle of 21 About how far does depression John IS SR down A 33 48 ft 3 3698 Ft C 22 35 ft D 35 42 Ft D the mountain 1210 ft X T 1200 Ft D

16 Squares Q R and I form with dimensions Q 13 what A 1241 59 m T R 20 m the area 29m a of B 441 Sq m D 21 sa m right triangle Square Q C 81 59 m

12 120 I lerstelimp3 fios as Imp9 timis To bulev TEXT 1 X H

Given 21 22 which similarity criteria proves that AABN AYXN Justify your thinking T B Ang If BN 12 AN 15 NX 32 find NY NY IS 25 The similarity criteria that proves AABW AYXN is SAS because they are vitical angles 12 15 NY 32 32 12 384 384 15 NY 16

In triangle ABC A 90 b 4 2 m and c 8 3 m Solve for B to the nearest degree

16 m 2 4x 2 68 2 1

Find the value of j in the diagram shown below Note Figure may not be drawn to scale 35 3 14 f x xX XXX 2 What is the measure of the bisected angle in the diagram J Heckad A

Choose the correct equation that models the Triangle Sum Theorem for this triangle 80 170 x 180 X x x 180 x x 80 180 x 80 180 Find the measure of the missing angle J Heckad A

Find the value of c in the diagram shown below Note Figure may not be drawn to scale x A 604 5c 9 f x x X XX VI TT What is the measure of each of the congruent angles in the diagram label optional

X a 11 Find BC 3a 7 1 TX X X X X 2 skill code 1612003

First try was incorrect Choose the equation that WILL NOT model the Triangle Sum Theorem for this triangle 31 118 2 31 x 180 31 90 x 180 90 31 x 180 x 31 90 180 Use any of the correct equations to find the measure of the missing angle label opcional

Which lists all of the cation that are equivalent to cos G FG and 10 W GH

Find each measure D E and F are midpoints of AB BC and CA respectively FD 90 B E 36 Y f x XX FC I X F 113

ch TODAY THIS WEEK CREDIT X A right triangle has a leg of length 10 yards and a hypotenuse of length 15 yards Find the length of the other leg Provide an answer accurate to the nearest tenth label required x f x X X r

3 The plane x y 2z 5 intersects the cone z x y in an ellipse Find the points on this ellipse with the largest and smallest distance to the xy plane

1 5 1 3 5 3 2 5 2 1 5 1 0 5 0 5 0 0 5 1 5 2 05 1 f x is concave up on 1 5 f x has inflection points at x 0 and at x 1 Of x has no local maximums 2 f x has a local mininum at x 0 2 5 0 1 3 U 1 00 3 5 J 0 f 0 4

The graph below is the function f x Find lim 2 3 2 2 3 Find f 2 si 5 5 f x Find lim f x z 2 Find lim f x 2

F C D H I H E Which angles are alternate interior angles ZFGD and ZEDG ZFGD and ZCDB ZFGD and ZEDB ZFGD and ZHGD

Geometry and estimate all the points that are 7 units away from the point 2 4 that cross the one y 1

Given FA Prove EA Step L FB FA 1 DB and FBI AC EB Statement FA FB FALDB FBLAC try Type of Statement Reason Given

A circle has a diameter with endpoints at A 1 9 and B 11 5 The point M 6 2 lies on the diameter Prove or disprove that point M is the center of the circle by answering the following questions Round answers to the nearest tenth one decimal place What is the distance from A to M What is the distance from B to M Is M the center of the circle Yes or no

4 50 78 4 points A Cessna P 210G needs to be modified so it will carry 100 gallons more fuel than a standard P 210G You are told to make 2 fuel tanks that will fit in the wings 50 gallons each You know from previous experience that the distance between the fore and aft spar is 4 6 1 2 and the wing is 11 3 4 thick How wide must each tank be Hint There are 231 cu in per gallon Find the volume of the tank first Then find the width of the rectangular tank using the volume formula 25 7 in 24 3 in 18 03 in

Find the value of x 10 x 5 2x 2

A circle has a radius of 3 inches What is the area of the shaded space Hint Find the of an area of the circle Within the quarter circle draw a line from the edge of the circle to the other side of this quarter circle forming a triangle Calculate the area of this triangle The shaded area is the difference between of an area of the circle and the area of the triangle 0 270 2 569 in 1 987 in 180 90

A square field which is 90 feet on a side is to be converted to a circular field of the same area What would the radius of the field be in feet 78 5 45 7 50 78

GARDENING A gardener uses a grow light to grow vegetables indoors If mz1 8x and mz2 7x 4 what is m21

Find the value of x Then find the measure of each angle 2x 3x 15 4x 16 2x

Find each measure 9 mz1 11 m23 12 m25 10 m22 12 MZA 14 m26 51 35 28

6 Given the right triangular prism below state whether the pairs of lines are parallel perpendicular skew or neither S A 6 00 S 7 Use the diagram below to match the given pair of angles with their correct names Alternate Interior Consecutive Interior Corresponding Congruent Supp 180 Congruent 8 7 m a TS and FE 2 b HF and HU c TH and UE d UE and SE A 22 and 26 ar B 28 and 25 are C 25 and 24 ar D 16 and 2 aro Alternate Exterior Congruent

3 Sketch the following curves in polar coordinates find the points of intersection and find the area of the region lying outside of r 2 2 cos 0 and inside r 5 cos 0

by which theorem DHF EHG F A ASA B SAS C SSS D HL can include 4x 8 3x 7 C ACQ bisects LACB What AB BIS C18 D 21 BEQ is the perpendicular bisector of Ab CmLQCB 26

which triangle is conginer to APQR J Q Sular A Def BUST CTLY

4 8 pts If y 9 and x 11 find CD and a CD y a X a B

1 A zip wire runs between two posts 25m apart The zip wire is at an angle of 10 to the horizontal Calculate the length of the zip wire O 25m O 10 25 4m 144 0m 141 8m 21 6m

4 Construct the sign chants of f x x 9x 7 x 2 3 then sketch the graph of y x x 7 x 2