Geometry Questions

RMV MVR Addition Property of Equality Vertical Angles Theorem Alternate Interior Angles Theorem Prove Find the measure of RMV Statement 1 FARM is a parallelogram m AFV 42 m FVA 117 2 FM AR 3 ZAFV ZMRV 4 m MRV 42 5 LFVA 6 mzMRV m2MVR mzRMV 180 7 42 117 m RMV 180 8 159 m RMV 180 Justification 1 Given 2 Property of Parallelogram 3 4 Transitive Property 5 Vertical Angles Theorem 6 Triangle Sum Theorem 7 Substitution 8

Question 1 Consider the Triangle XYZ Y 1 3 2 1 0 N T Z 1 4 3 4 5 6 X 4 2 Triangle XYZ is reflected over the y axis to create X Y Z and then translated by the rule x y x 4 y 3 to create X Y Z Write the coordinates for Triangle X Y Z and Triangle X Y Z Express your answer as an ordered pair X Y i X Y 7

16 3 eesees A 9 3 If AB has length 9 3 and AC has length 16 3 find The length of BC The measure of angle B in degrees The measure of angle C in degrees B If you use a calculator to find a decimal approximation your answer must be accurate to at least 3 decimal places

13 9 A AC has length 13 9 and BC has length 16 1 find The length of AB The measure of angle B in degrees The measure of angle C in degrees 16 1 B you use a calculator to find a decimal approximation your answer must be accurate to at least 3 ecimal places

solving the triangle A ZA LB ZC b 31 586 38 942 degrees degrees degrees C a 5 b 6 C 9

11 67 A ngle C measures 67 and AC has length 11 find Angle B in degrees 23 The length of AB The length of BC B ou use a calculator to find a decimal approximation your answer must be accurate to at least 3 imal places st be sure that your calculator is set to degrees not radians

Find the reference angle create a tr the hypotenuse of your triangle 1 u 5 555 y

8 220 AM

d all angles and sides of the triangle C 6 95

555 310 X

Calculate the surface area of to volume ratio for the following two spherical cells Cell A r 3 cm Cell B r 7 cm Show your work Length of Sides cm Surface Area cm Volume cm SA V Ratio RELEVANT EQUATIONS r radius length h height w width s length of one side of a cube Volume of a Sphere V 4 3 r

x 4 m x x 2

b x 56 67 67

2 7149 150 150 the volume 7 5556

find x 1 2t the an d for the plane parallel to the line and that contains z 1 2 t x 3y 77 2 an equation for y 2 3 t line of intersection of the planes 3x 1ly 172 2

Find the Surface Area and Volume of the following triangular prism 27 13 12 14 15 16

X 17 60

5 Find an equation that gives all points P x y such that the absolute value of the differences of the distances of P to 1 3 and 1 9 is always 4 Your answer should be a b 1 j k where a b j and k are constants in the form

9 130

380

240

650 X

7 715

3MK 24 JL 20 and m2MJL 50 K M W L NK NL ML JM m2KNL m2KJL m2MLK m JKM m2JML

In AABC m C 45 If point D is the midpoint of AB and point E is the midpoint of BC what is the measure of ZADE

4 Convert the expression

Find the reference angle create a triangle and find all angles and sides of the triangle Consider the hypotenuse of your triangle 1 unit 5 7 290 et 715 X 6 8 240 380 X 0803

Part A eflect G and F across the line x 7 Label the images with prime notation Then draw quadrilateral GG F F 10 G 10 Part B Give the most precise name for quadrilateral GG F F Explain WHY IT IS the figure you named by explaining how it meets the definition of the figure The most precise name for the figure is because

Find the length of side x Round to the nearest tenth X 6 5 X 68 5

Geometry 8 Tell whether a triangle can have sides with the given I a 11 17 28 b 3 10 11 9 Describe the possible lengths of the third side of the triangle given the lengths of the other two sides a 16 inches 20 inches b 8 meters 12 meters c 5 feet 14 feet 10 List the angles of the triangle in order from smallest to largest a b 21yd D V 8 yd 15yd F B 57 E 77 46 Q 11 List the sides of the triangle in order from smallest to largest b a C 10 cm 12 cm H 95 R 419 6 cm 44 P F C C U 20 ft 3 1259 W 24 f 219 21 ft K L V

Find the area of the parallelogram with vertices A 1 1 4 B 0 3 9 C 1 0 7 and D 2 2 12 Area

Geometry 4 Point P is the centroid of AABC Find the indicated measurement a CD AP 3 mZ1 G AL 18 Find AP and PL 5 Find the missing length indicated SHOW WORK IF POSSIBLE a b 21 7 Complete the statement with or 1 AC DF A 24 118 E D m22 PL 20 H L 120 18 b BP 80 Find PL and BL PL 2 mZHGI S 3x 9 BL 4 KL MN B SR B x 7 K m IGJ G A H 9 1 9 30 21

What is a sequence of transformation to describe the figures in the graph 10F 8 C B A 864 2 2 A 2 4 6 B 8 10 Rotate 90 clockwise about the origin then Reflect over the y axis Rotate 270 counterclockwise about the origin then Reflect over y x Translate right 2 then Reflect over the y axis Reflect over the y axis then Translate right 2

Toets H3 Wortels Opgave 1 6 punten Schrijf zo kort mogelijk en vereenvoudig indien mogelijk je a 4 2 3 2 5 b 2 3 3 9 c 3 3 2 12 d 3 12 27 e 7 2 3 Opgave 2 5 punten Schrijf de wortels als een wortel met alleen een getal onder wortelteken C 2 13 a b 5 3 2 5 Vereenvoudig indien mogelijk d 2 90 e 3 50 f10 8 Opgave 3 5 punten In de figuur zijn alle hoeken recht a Bereken de omtrek van de figuur Geef een zo kort mogelijk antwoord 2 2 3 6

Match the following drawings with the fitting s you would use 14 90 elbow a 15 Wye 45 b 16 45 elbow 45 elbow C 17 4 0 Wye d

Solve for x Round your answer to the nearest tenth 70 T 6

19 yd 16 yd DO SUL TO 39 7 15 2 yd

4 7 ft 34 ft 10 ft 27 ft 19 ft 11

28 m 28 m 22 1 m 3

20 m tr 20 3 m 12 m 13

Assignment 5 17 points Given is the following optimization problem max 5x1 3x2 S t X1 12 10 01 2x2 36 3x1 x2 24 21 12 0 5 a Solve this problem graphically Draw the constraints and objective shade the region of feasible solutions and find an optimal solution by moving a ruler parallel to the objective function b Find an optimal solution using the two phase Simplex method When several variables could enter of leave the basis always select the one with the smallest index

16 A line segment has endpoints 2 7 and 5 4 The line segment is dilated by a factor of 3 around 4 3 What are the new endpoints and length of the line segment

1 Use the given values to evaluate if possible three trigonometric functions cos x csc x tan x 1 sin x cos x 0

4 Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of 0 where 0 x 25x 36 5x 6tan

2 Use the given values to evaluate if possible two trigonometric functions tan and csc w cot 5 sin w 10

1 Hints All trapezoids have two pairs of consecutive supplementary angles Trapezoid Property All trapezoids have at least one pair of parallel sides Isosceles Trapezoid Property Sides All isosceles trapezoids have at least 1 pair of opposite congruent sides legs Isosceles Trapezoid Property Angles All isosceles trapezoids have 2 pair s of consecutive congruent angles Isosceles Trapezoid Property Diagonals The diagonals of all isosceles trapezoids are congruent P Triangle Angle Sum 180 Alternate Interior Angle Theorem T 76 34 R 73 410 A Vertical Angle Theorem Same Side Interior Angle Theorem 2 P 21 97 45 65 thir an Isosceles Trapezoid Yes or No agonal Is this an Isosceles Trapezoid Yes or No

Rectangle AE mLABD m2DAE A 20 EB 5m MLADE mzBAC B Woled Caugh audmona Square to cemuzeem D DE mLABD mLACD 7m AE C mLAED m DBC

Find the missing side lengths and angle measures indicated for the figures below Parallelogram D mLABD A EB 725 mLDAC 30 35 7 cm E 72 5 72 6 cm AE 35 m2ACD 80 MLADB Rhombus EB mLABD m2BAE D 30 9 cm 46 cm C AE B m AEB MLADE

Find all missing side lengths and angle measures of the figures below Parallelogram Rectangle 71 8 cm 10 ft 3 cm GOAsin HW 4 ft Rhombus Square Thurs 4 cm 5 m 101

State the most specific name for each figure or 1 3 5 7 30AM 3A8AM 2 4 6 8