Geometry Questions

Find the area and perimeter of the shaded figure below 1 unit 1 unit Area Perimeter square units

A rectangular paperboard measuring 20 in long and 12 in wide has a semicircle cut out of it as shown below What is the perimeter of the paperboard that remains after the semicircle is removed Use the value 3 14 for x and do not round your answer Be sure to include the correct unit in your answer 12 in 20 in in X in2 3 in

Find the area of the figure Sides meet at right angles 3 in 3 in 3 in 3 in 17 7 in 3 in 7 in 9 in

Find the area of the figure Sides meet at right angles 4 ft 5 ft 4 ft 2 ft 4 ft 2 ft 5 ft 0

Find the area of the figure Sides meet at right angles 4 m 5 m 4 m 4 m 4 m 5 m 4 m

List the sides in order from least to greatest measure 12 T 13 N 14 B S 24 137 19 38 98 445 P C 55 35

Lines BE FC and AD intersect at G Replace each with or to make a true sentence 18 m BGC 19 m BGC 20 mLAGC mLAGC mLFGE m CGE B G 43 82 to F E Exercises 18 28 D

Refer to quadrilaterals QRST and FGHJ 13 Name a side that is consecutive with RS 14 Name the side opposite ST 15 Name a pair of consecutive vertices in quadrilateral QRST 16 Name the vertex that is opposite S 17 Name the two diagonals in quadrilateral QRST 18 Name a pair of consecutive angles in quadrilateral QRST 19 Name a diagonal in quadrilateral FGHJ 20 Name a pair of nonconsecutive sides in quadrilateral FGHJ 21 Name the angle opposite ZF R Q S Exercises 13 18 F H G

List the angles in order from least to greatest measure 9 E 10 11 X 9 cm D 15 cm 12 cm 3 0 m G 1 1m H 2 0 m 28 ft 19 ft 21 ft

24 In the diagram below of circle O tangent AB is drawn from external point B and secant BCOE and diameter AOD are drawn E B If mZOBA 36 and OC 10 what is the area of shaded sector DOE 3 1 3 10T 10 2 37 4 15

2x 20 Equation 6x 24 Angle Type Alternate Interior r S

answering the questions below 35 54 90 Triangle NYE angles of a triangle and the lengths of the sides opposite them be SQUIT F T 1380 810 Measures of the Angles mich INAY HDZF 1640 well mal 20 PU 480 FY LF LY TU QT QU MG 1030 G Lengths of Sides Opposite the Angles M

Replace each with or to make a true sentence 18 D 19 G H 20 3 E m43 m 1 75 MLG 75 K M Co m48 m26 m27

5 The pedal triangle for AABC is obtained by joining the feet of the altitudes What happens to the pedal triangle if for example is a right angle

15 10 5 0 5 10 15 20 Exercises 12 17 Replace each with or to make a true sentence 13 HK OK 12 MT JT 14 JU OS Determine if each statement is true or false 15 MHZ JS 16 HTTM 17 KH U

Identify the angle with the greatest measure 15 K 2 3 km L 16 7 6 km 5 8 km M 19 in B J 16 in 14 in Z 17 T 6 mi R 5 mi 155 N

In the diagram below draw the two limiting parallel lines to the given line I and a point P on the Poincare model of hyperbolic geometry Indicate the two angles of parallelism for I and P

Write an equation of the line below K 8 7 6 5 4 3 2 2 8 6 S 4 2 23 6 7

Determine whether each pair congruence statement and explain why the triangles are congruent 13 A 12 14 B E 15 BD

Find the surface area of the figure below to the nearest foot Be sure to label the unit 5 is the hypotenuse of the triangle I 5 ft Z fo 6 ft

In AMNP NS bisects LMNP MR bisects LNMP and PQ bisects LMPN 12 Find m24 if m23 31 13 If mLMPN 34 what is m26 14 What is m 3 if m2NMP 64 15 Find m MNP if m 1 44 16 What is m 2 if ZMNP is a right angle 17 In AXYZ YW bisects ZXYZ What is mLXYZ if m 2 62 18 Algebra In ADEF EC is an angle bisector If m CEF 2x 10 and m DEC x 25 find m DEC X Q N 3 2 O S R 12 W

Graph the region R bounded by the graphs of the equations Use set notation and double inequalities to describe R as a regular x region or a regular y region whichever is simpler y x3 y 3 2x x 0 Use the graphing tool to graph the region R Click to enlarge graph Describe R as a regular x region or a regular y region whichever is simpler Choose the correct answer below and fill in the answer boxes to complete your choice OA R x y h y x k y OB R x y g x y f x sys where h y x where g x and k y and f x 2 1 5 Ay 4 3 2 4 4 2 3 4 5

H PAR 49 G Which statement best explains the relationship between lines FG and HJ O They are perpendicular because their slopes are equal O They are perpendicular because their slopes are negative reciprocals O They are not perpendicular because their slopes are equal O They are not perpendicular because their slopes are not negative reciprocals

Determine whether each pair of triangles is congruent by SSS SAS ASA or AAS If it is not possible to prove that they are congruent write not possible 19 A 21 B R K C E S 20 F E G 22 T U X H

9 AABC is right angled at A and has AB AC Point D is on AC so that AB AD Point L is the midpoint of AD Let P be the point on the circumcircle of AADC so that ZAPB 90 a Prove that B P L and A are concyclic b Prove that LLPC 90

3 Amazing Diagram Find the area of ACDE A D a 0 C E H ACDE b 02

What are the coordinates of J if the given triangle is dilated with a scale factor of 2 about the origin B 7 3 A K OJ 1 3 OJ 3 5 OJ 5 7 TULC 60

13 Following is the graph of f x x Describe the vertical horizontal translations and the vertical stretch or compression and sketch the graph y g x 3 x 2 1 Label the new positions of points A B and C after the translation on the graph of y g x

Is there a basis B of R2 such that B matrix B of the linear transformation T J is upper triangular

r 17 19 Use the sketch below to find each of the following 6 points 90 C ARE L AR

In the applet below h represents the terminal point s horizontal distance to the right of the circle s center in radius lengths You can vary the value of h by dragging the purple X on the horizontal diameter of the circle The angle s whose terminal point is h radii to the right of the circle s center is are shown 0 30 a Set h to about 0 5 How many radian angle measures 0 between 0 and 7 correspond to this value of h b Set h to about 0 7 How many radian angle measures 0 between 0 and 7 correspond to this value of h c Given any value of h can you determine exactly one corresponding radian measure 0 between 0 and V

6 CE 8 6 20 2 6 8 N Sequence 1 Figure 1 Is first reflected over the line y and then translated 8 units up and 2 units right to create figure 2 co Which two sequences of transformations could be used to prove figure 1 and figure 2 are congruent Sequence 3 Figure 1 is first reflected across the x axis X Sequence 2 Figure 1 is first translated down 10 units and then rotated 180 clockwise about the origin to create figure 2 Sequence 4 Figure 1 is first rotato 009

Which of the following statements about JK and JL is true 8 7 y 6 5 4 3 2 4 J 2 4 K 7 8 2 3 4 5 678 L 1 1 X A JK is 9 units long OB JK and JL are the same length OC JL is longer than JK O D JK is longer than JL

The circle have the same radius r while the large square is of length 1 Find the value of r up to 3 decimal places A 0 183 B 0 185 C 0 189 D 0 191

Find the length of CD 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 C 3 2 D 7 8 O A About 7 2 units B 10 units OC 52 units OD About 3 2 units

Find the volume of the figure below to the nearest millimeter Use the it in your calculator Be sure to label the unit 6 mm 12 mm 12 mm 7 mm 12 mm 12 mm 6 mm

in the list below determine whether or not each example is a rigid motion If it is a rigid motion identify the type of transformation 6 points Example Flipping a pancake Deflating an air mattress Moving a clock s minute hand nlarging a photo ing a golf ball Rigid motion Yes or No If yes what type of rigid motion

11 If m A 2x 5 and m C 3x 20 what is m A and m C 3 points D I

A fish tank has a volume of 8 3 tt Use the table of conversion facts to find out how many gallons of water it would take to completely fill the fish tank Round your answer to two decimal places Conversion facts for volume and 1 cubic yard yd 201 97 g 1 cubic foot 7 48 galle 231 cubic inches in I gallon Note that means is approximately equal

To receive full credit for the following questions show as much work as possible 16 PR and QT are diameters of OA Find each measure A mRSU B mPQS U P 40 50 40

40 In the figure C is the mid point of BD LACB 50 and ZABC 90 Find LADC correct to the nearest degree A B A 23 B 25 C 28 D 31 50 C D C

Find the area of the kite below to the nearest tenth Be sure to label the unit 5 cm 3 cm 3 cm 3 cm

Use n 10 and p 0 7 to complete parts a through d below a Construct a binomial probability distribution with the given parameters P x 0 2001 0 2668 P x 0 0000 0 0001 0 0014 0 009 0 0368 5 0 1029 Round to four decimal places as needed X 0 1 2 3 4 X 6 7 8 9 10 0 2335 0 1211 0 0282 b Compute the mean and standard deviation of the random variable using x Hx 7 00 Round to two decimal places as needed ox Round to two decimal places as needed h Ex P x and ox X P x H

A 8 OA ZA and B OB AB and BC O C ZA and C O D BC and AC C

Consider the following figure N c NP M d QS R Find the following a mZN in degrees b mzP in degrees Given AMNP AQRS mzM 69 m R 78 MN 6 QR 4 RS 7 MP 11 O S O P

1 Using the picture below which statements are TRUE select 2 choices H D F G and H are coplanar J G D and H are coplanar D G F are collinear G F H are collinear

Given that m ABC 15 find m BCD A E D C diagram is not drawn to scale m BCD B

What are the sides of APQR O A P Q and R OB PQ QR and PR OC None of these O D LP ZQ and ZR

What function is graphed below Oy cot Oy cot 6 4 2 6 x

13 Given LAE LC CF AD Pww AE CE D B F