Geometry Questions

Given A EFG RSQ Which statement is true Select one O O EF RS FG SQ EG RQ EF RS FG SQ EG RO EF FG ORE 0 RQ RS SQ EG

Find the recursive definition of this sequence 4 9 14 19 an 3an 1 a 5 B an an 1 9 a 4 C an an 1 5 a 4

The angle bisectors of AEFG are ES FS and GS They meet at a single point S In other words S is the incenter of AEFG Suppose QS 6 FS 13 mZQGR 34 and m PFS 26 Find the following measures Note that the figure is not drawn to scale E P F R S Q G RS m2PFQ m PES 00 X

The angle bisectors of APQR are PZ QZ and RZ They meet at a single point Z In other words Z is the incenter of APQR Suppose WZ 12 PZ 21 mZWPY 42 and mZYRZ 18 Find the following measures Note that the figure is not drawn to scale W Q Y X R mZYRX mZxQZ XZ 00 X 20

Challenge 2 A ski lift forms a right triangle as shown Use the Pythagorean Theorem Theorem 9 1 to approximate the horizontal distance traveled by a person riding the ski lift Round your answer to the nearest whole foot 1170 ft 5750 ft

Consider quadrilateral WXYZ below W Z X 4567 8 9 Y Note that WXYZ has vertices W 4 2 X 1 3 Y 4 4 and Z 1 5 Complete the following to determine if WXYZ is a parallelogram

Which of the following are reasons used in the proof that the angle bisector construction can be used to bisect any angle Check all that apply A A CPCTC B Any line segment can be extended indefinitely C All of the radii of a circle are congruent D SSS triangle congruence postulate

In circle E the measure of the indicated angle AEC is 243 5 Lines AD and DC are tangent lines The m AEC The measures of angles EAD and ECD are The mzABC A D The m ADC E 4 2435 B C

Find the area of the parallelogram 4 m F 10 m m 5 5 m 2

The triangle circumscribes the circle What is the perimeter of the triangle A 4 cm 5 cm Select one O a 25 cm Ob 24 cm O c 25 5 cm O d 37 5 cm B C 3 5 cm

Find the value of x Round your answer to the nearest tenth 8 5 X Select one a 12 5 O b 9 4 O c 6 2 O d 18 9

Find the value of y 160 A T B C 136

B A 100 m x mCD mAB P Find the value of x Select one O a 34 O b 50 O c 66 O d 32 D 32

SA 4tr What is the surface area of the sphere 10 in Select one O a O b O c O d 100 in 100 in 400 in 500 3 t in

Length of a circular arc Length of AB 2mr Find the length of AB Round your answer to the nearest tenth A 8 in Cougar 100 B Select one O a 55 9 in MAB 360 O b 14 0 in O c 50 3 in Od 20 9 in

V h Find the volume of a cone with diameter 16 cm and height 12 cm Select one O a 100 5 cm O b 3217 0 cm O c 2412 7 cm O d 804 2 cm

Area of a sector A degrees in corresponding arc 360 Find the area of the sector 9 cm Select one 80 a 18 cm O b 9n cm O c 12 cm O d 4 cm

Consider quadrilateral JKLM below 9 8 7 5 54 3 M L Length of JM J Note that JKL M has vertices J 4 6 K 8 1 L 3 2 and M 1 3 Complete the following to determine if JKLM is a parallelogram Length of KL 0 K a Find the length of JM and the length of KL Give exact answers not decimal approximations

5x 2 X 6x Find x if the given figure is parallelogram

Area of a trapezoid 1 2 b1 b2 h Find the area of the trapezoid below Round your answer to two decimal places 20 3 cm 8 9 cm 25 cm Select one O a 730 cm O b 401 8 cm O c 403 17 cm O d 201 59 cm

L 70 0 M What is the measure of angle LMN if the figure is a trapezoid degrees

L 2x 3 X 4x 21 M N What is the value of x is the figure is a rectangle

What is the sum of the measures of the interior angles of the figure below M Q Select one O a 900 O b 540 O c 360 O d 720 N P

Select one Oa measure of arc BC 39 4 b Oc 90 measure of arc BC measure of arc BC 140 6 measure of arc BC 70 3 E P 140 6 A B

B A 5 C b Find the value of x to the nearest tenth 8 Select one sin A a cos A b C A tan A 2 2 O a 51 3 O b 38 7 O c 32 0 O d 58 0

Find the value of x Leave your answer in simplest radical form X 13 11 Select one O a 4 3 O b 8 6 O c 24 2 O d 16 3

B Q C b sin A a C cos A A tan A Select one or more Ocos 48 x 14 sin 42 x 14 sin 48 x 14 Which equation s can be used to find the value of x Choose all that apply A 14 42 cos 42 14 x b C

In spherical geometry lines are called O A great circles OB radii O C line segments O D diameters

ect one a segment AE 12 b segment AE 10 segment AE 14 5 d segment AE 14 A What is the length of segment AE B E 15 8 D 10 C

ect one a mzDEC 114 b m DEC 66 cm DEC 57 d m DEC 123 The measure of arc AD 42 and the measure of arc BC 72 What is the m2 DEC 42 D A E F B 72 C

Select one Om BDC 86 Obm BDC 43 Om BDC 107 Od m BDC 73 150 A What is the m BDC F 64 B D

ect one a mzBEC 71 b m BEC 82 cm BEC 142 d m BEC 41 The measure of minor arc AD 112 and the measure of minor arc BC 30 What is the m BEC 112 A D 14 B 30 E

The measure of the inscribed angle BEA 67 8 What is measure of major arc BEA B E lect one a The measure of major arc BEA 292 7 b The measure of major arc BEA 135 6 The measure of major arc BEA 112 7 Od The measure of major arc BEA 224 4 67 8

elect one a AC 6 Ob AC 8 Oc AC 12 O d AC 10 If AD 5 units BE 6 units and BD 2 units what is the length of chord AC E A D 90 B C

ect one a segment DC 23 b segment DC 30 C segment DC 32 d segment DC 25 A D What is the length of segment DC 28 B 8 LO 9 E

lect one a arc length of major arc ABC 28 2 b arc length of major arc ABC 27 5 Ocarc length of major arc ABC 29 1 Od arc length of major arc ABC 28 6 1 What is the arc length of major arc ABC 8 D 1972 B C

elect one a O b 3 Oc 3 O d K What is the measure of the indicated arc in radians 135

b The mzBEA 41 3 What is the measure of minor arc BA B ct one a measure of minor arc BA 41 3 E C measure of minor arc BA 97 7 measure of minor arc BA 82 6 d measure of minor arc BA 138 7 41 3

Select one O a m2BDC 36 O b m2BDC 40 Ocm BDC 18 O d mzBDC 42 If the m ABC 18 what is the mzBDC B A C D

elect one O a 2 O b 3T OC 6T O d 4 What is the length of the indicated arc in radians if the radius of the circle is 4 135

D is the centroid of AABC What is the value of x when GD x 4 and GC 4x 5 G F B D E C

AABC is rotated 180 about the origin and then dilated by a factor of 2 using the point 4 6 as the center of dilation What is the transformation of C 2 4 65432 OR 4 3 N 2 2399 C 2 4 B 5 3 O A C 1 1 O B C 1 0 O C C 1 1 O D C 0 1 A 3 1 2 3 4 5 6

A walking path BE in a park intersects two sides of the park at their midpoints You walk from point D to E from E to B from B to C and back to point D How many yards did you walk A 254 yd yards B 74 yd NE 107 yd D

ABCD is a parallelogram Which statements are true B y 3 17 x 5 72 D The value of y is less than 72 O The value of x is a factor of the value of y O The value of y is three more than a multiple of x The value of y is at least six times the value of x

Determine the value of x in the diagram 3x 3x

A circus owner wants to place an ATM at a location that is equidistant from the three main tents at points D E and F Which of the following can be used to determine where to locate the ATM O the medians of ADEF O the altitudes of ADEF O the angle bisectors of ADEF O the perpendicular bisectors of ADEF

Determine whether each statement is true or false 113 KL NM M P KL NM 114 N m MPN m LJK True O False O

rite an equation of the perpendicular bisector of the segment with the endpoints 8 1 and 4 5

SOHCAH TOA mnemonics device for remembering right triangle trig ratios Sine is ratio of sides Opposite over Hypotenuse B cos 32 1 Which equation associates an acute angle to a valid ratio of side lengths A sin 380 AB C tan 90 d ale ale le cl D sin 52 1 11 III A I only B III only C I and II D II and III SOH CAH TOA AB Cosine is ratio of sides Adjacent over Hypotenuse 2 Given the right triangle ABC below which of the following is equal to b sin A cos B tan A Tangent is ratio of sides Opposite 38 B a over Adjacent 40 ft 52 B b 25 ft

Two airplanes are flying parallel to each other on paths that are described by position d and time t The variable d is measured in miles and the variable t is measured in seconds The equation describing the graph of the position of the first object with respect to time is d 3 67t 4 81 The graph of the position of the second airplane is a parallel line passing through t 0 d 2 14 What is the equation of the second graph Select one O a d 4 81t 2 14 O b d 4 81t 3 67 O c d 2 14t 4 81 O d d 3 67t 2 14