Geometry Questions

the following problems using Pythagorean Theorem Round to the nearest tenth where necessary Always include units in your answer For example if you answer is 100 feet write 100ft Question 6 2 points Listen If a rectangular soccer field has length of 240 meters and width of 70 meters How long is its diagonal D 70 m 240 m

In an isosceles triangle ABC with AB AC the bisector of angle C meets side AB at D if BC AC AD then A ZA B C T 3 3 8 C length of angle bisector CD 4 2 2 AB cos D length of angle bisector CD 4 2 2 AB cos RO ROO 8 TC 8 N REDMI 7 CAMERA

f 1 cose sine sine 1 cose 2csc0

x a 5 x 6 7 x fonksiyon ise f 2 a b bir sab f x fonksiyonunu bulunur

1 Follow the steps below to help you prove or disprove that the point 1 15 lies on the circle that is centered at the origin and contains the poin 0 4 To earn full credit you must show your work Step 1 Plot a point at the origin and at 0 4 Use these to help you draw the circle centered at the origin that contains 0 4 Step 2 Determine the radius Step 3 Use the radius and the coordinates of the center to write the equation of the circle Step 4 Substitute the x and y coordinates of the point 1 15 in the equation of the circle to check whether they satisfy the equation

A hot air balloon is floating above a straight road To calculate their height above the ground the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon The angles of depression are found to be 16 and 19 How high in feet is the ballon Hint

Find the value of y K Fro 28 H

Find the circumcenter of the triangle 15 10 86

Find the value of x 84

Use the figure at the right If JK 7x 16 and NO 15 what is the value of x N HE L M K

In ADEF the midpoint of the side opposite vertex D is M and the centroid is C If DM is 21 what are DC and CM DC 14 units CM 7 units

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