Geometry Questions

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

3 Find m PST Q P S 11x 3 5r 9 T H

From the last problem we figured out that x 12 23 38 24 83 25 59 Now it is time to describe some of the other angle relationships m2MAY Select all that apply 23 24 28 25 24 25 142 0121 by the Angle Addition Postulate M B 3 Q S A R

Find the area of the regular octagon below Round to the nearest centimeter Be sure to label the unit 3 cm 2 5 cm

Find the approximate value of using the trapezoidal rule with four subdivisions Draw a graph to illustrate The estimated value is Give your answer accurate to four decimal places This answer is an x dx 3 under estimate over estimate Explanation of answer above because the function is concave up because the function is concave down because the function is increasing because the function is decreasing

ind the area of the regular pentagon below Round to the nearest meter Be sure to label the unit 4 9 m 7 1 m

If A B and I are collinear and AC 24 find AB and BC A 2 x 5 B X 2 C

Given AC bisects LCAB 60 Prove LDAB 120 L DAB A D C B

Given LADBE LCBD LCDB LABD Prove AABRE D ACDB A D B

The two triangles below are similar 15 I 36 40 10 104 K X 40 18 104 30 20 W Complete the similarity statement AUK A What is the similarity ratio of the first triangle to the second triangle Simplify the similarity ratio and write it as a proper fraction improper fraction or w number

8 Which triangles are congruent and by what theorem you can just give the names no proof needed for this one Find x and y A E 2x ry B 4x 10 D Sx 15 C F

Given CD is a median AC BC Prove LACD LBCD A D B

Find the supplementary angles A C 2x 30 5x10 D B LADC and LCDB

A Find x y and z if LABC ADEF 5 x E Z 11 F

2 3 Indicate three different bases for the following three congruent triangles and draw in the perpendicular height for its base on each shape Now measure in centimetres to one decimal place for each triangle the base and its corresponding perpendicular height and use the table provided to calculate the area of the triangle using the formula Area of A base X1 height A ABC Triangle Base A B C B3 A2B2C2 B1 C3 C A2 B2 Perpendicular height Area C

70 99 a Enter the values of the exterior angles for this quadrilateral in the table and calculate the sum b Drag the points to create two new quadrilaterals and complete the table for both of these c Move to the next slide and do the same for a pentagon What do you notice What do you wonder A B C Sum of Angles

Which side lengths form a right triangle Choose all answers that apply A 2 3 4 8 3 17

What other polygon do you see in the design What is the polygon with the most number of sides that you can find in this design