2D Geometry Questions and Answers

calculate the measure of angle B F 55 N 20 45 DP B 50

1 a Here we see part of the curve given by 2x y sin Find the tangent line to this curve at the point 1 1 X 2 b Let y a b be any numbers Show that at any point where the curve xy a ntersects the curve x y b the two curves are perpendicular on gach other

Find the intersection points of the parabola y 2x x 1 and the line x y 3 Give your answer as two ordered pairs separated by a comma For example if you found that the solutions were 1 2 and 3 4 you would enter 1 2 3 4

The diagonal of a square measures 17 units We want to find the perimeter of this square 20a First find the exact side length S of the square with a rational denominator 20b S 17 2 Hence find the perimeter of the square Perimeter Enter your next step here

Consider the triangle below 9a Find the exact value of b 18 b 45 C

Consider the triangle below b a 10 60

Consider the triangle below a Find the exact value of b b 11 2 45

Da The diagonal of a square measures 17 units We want to find the perimeter of this squal First find the exact side length S of the square with a rational denominator

4 Which pair of angle measures would NOT allow you to calculate each of the angle measures of the inscribed quadrilateral

4 Right triangle GHL has mLL 90 HL 1 and GH 2 Draw the triangle then identif below i ii sinH tanG cos H

2 Write the following trig ratios for the triangle below Simplify your ratios a sin A b cos C c tan A C f d tan C e sin C cos A C 34 A pien 30 16 B wris

What is the volume 1 mm 2 mm 2 mm cubic millimeters

What is the volume of this cylinder Use 3 14 and round your answer to the nearest hundredth 10 mm 10 mm cubic millimeters

Find the measures of the lettered angles 4 57 d e f g 2 A 5 in 21 22 p m 180 180 185 1454 n 3 M 2 6 b 80 20 m21 21 22 m42 20 11

FAST WORKERS Find the missing angle measures in the triangles below 65 40 57 85 50 20 130

1 For the function y x 8x 12 a b d e f g Partial credit will be given as warr A scale must be shown on each axis of each graph Follow the directions for each part of the problem precisely x Does the function open upward downward Write the y intercept as an ordered pair Use quadratic formula to determine the x intercepts and write as ordered pairs b nac 20 Write the y in 6 201 leath anored pa Write the function in vertex form by using the vertex formula 3 0 12 Write the vertex as an ordered pair Write the axis of symmetry X Sketch the function Label the vertex and intercepts on the graph

1 Use the triangle below to answer the following questions Hint Draw an arrow to visualize Which side is across from angle B A Which side is across from angle A Which side is across from angle C KEY UNDERSTANDING B C

5 In AEAC determine the following sin E cos E tan E sin C cos C E 2 A 45

1 In the diagram above of AJKL JL 7 KL 2 Determine the following ratios Write your answers in simplest radical form J sin L cos L sin K

YOU DO ROUND 1 1 In right triangle DEF below FE 3 and DE 4 Determine sin D a b cos D C tan F E LL F

3 In right triangle ABC below which of the following ratio s is greater than 1 a sin A b sin C c tan A d tan C A 15 17 B 8

4 Cassie simplified the composed function f x cot arcsin x Her work is shown below 1 point Step 1 f x cot A where A arcsin x and x sin A Step 2 sin A opposite X hypotenuse 1 Step 3 adjacent 2 1 2 Step 4 cot A opposite adjacent X In which step did Cassie make her first error Review Guidelines If you guessed the answer to this question or did not answer it correctly go back and review composition of functions C 0 pts step 1 C 0 pts step 2 X 0 pts step 3

A cylinder has a volume of 1in and a radius of in What is the height of a cylinder Approximate using inches inches inches

2 In the figure JKLM EFGH Complete the following table E y H Value of x Value of y 8 Scale factor of JKLM to EFGH Value of 2 3 G 11 F 20 K X Note i Figures not drawn to scale ii Use slash to separate numerator and denominator wherever needed 30 L Z

6 The following image shows four polygons Select all of the figures that are scaled copies of polygon ABCDE B D A K E A polygon KLMNO B polygon PQRST C polygon FGHIJ E N 0 6 Q P S

1 The two figures are proportional Find the value of x A 24 in B 40 in 12 in D 30 in 36 in X 12 in 10 in

If the following shapes are similar then find the measure of the missing length g Type your result in the empty box provided below 12 in 6 in Note Figure not drawn to scale inches 1 in

Examine the pair of triangles given below If AEDC AKGH then the value of ZK is H E 56 C 34 G K

onsider the following figures in which AABC ADEF Find the scale factor of AABC to ADEF in both figures shown below Figure 1 B B 15 Figure 2 A Scale factor 10 18 16 Scale factor 20 2 5 0 4 12 C C E E 25 A 10 40 12 50 8 F

estion 4 Multiple Choice Worth 2 points lume of Cylinders MC denton Bakery is baking a cake for a customer s qui hes

The two rectangles are similar Find z 24 14

Suppose a company has a water cooler cooler that is currently holding 470 cubic inches of water They have paper cone shaped cups each with a height of 3 inches and a diameter of 3 inches How many whole cups can be filled to full capacity before the water cooler is empty Enter your answer as a whole number

44 13 2 Show your work here are similar Find 7 7 2 136 n

Given AABC ADEF X 3 B A 2x 1 C E 4 6

Given the similar quadrilaterals 116 73 6 What is the value of y A 166 B 189 C O 134 D 93 619 116 5

Find the missing length indicated k O 100 O 400 O 144 O 169 192 X 256

Find the values of x y and z 8 16 O x 32 y 16 5 z 8 5 Ox 24 y 18 z 16 Ox 24 y 9 6 z 6 15 O z 28 y 12 6 z 8 3 O None of the other answers are correct

Find the missing lengths 0 5 2 O 20 O 15 O 15 2 45 60 10

Find the missing lengths O 11 6 2 O 22 2 O 22 3 O 22 3 11 50 45 X

Find the missing length indicated 65 25 O 144 O 200 O 289 O 169 X

One leg of a 45 45 90 triangle measures 12 centimeters What is the length of the hypotenuse O 4 3 cm O 6 2 cm O 12 2 cm O 12 3 cm

A community is building a square park with sides that measure 110 meters To separate the picnic area from the play area the park is split by a diagonal line from opposite corners Determine the approximate length of the diagonal line that splits the square Round your answer to the nearest tenth O 110 meters 24 200 meters 220 meters 155 6 meters None of the other answers are correct

Find the missing side length Tell if the side lengths form a Pythagorean triple Explain 25 20 The missing side length is 15 The side lengths form a Pythagorean triple because they are nonzero whole numbers that satisfy the equation a b c 2 The missing side length is 32 02 The side lengths do not form a Pythagorean triple because one of them is not a nonzero whole number The missing side length is 5 The side lengths form a Pythagorean triple because they are nonzero whole numbers that satisfy the equation a c The missing side length is 32 02 The side lengths form a Pythagorean triple because they satisfy the equation a b c O None of the other answers are correct

18 5 10 5 1 P 10 S en the graph of f x above find the following and write your answer in interval notation Domain of f x Range of f x

A hummingbird lives in a nest that is 3 meters high in a tree The hummingbird flies 5 meters to get from its nest to a flower on the ground How far is the flower from the base of the tree meters

John leaves school to go home He walks 6 blocks due North and then 8 blocks due west How far is John from the school blocks

A rectangular carpet measures 7 feet long and has a diagonal measurement of 74 feet Find the width of the carpet feet

The main mast of a fishing boat is supported by a sturdy rope that extends from the top of the mast to the deck If the mast is 20 feet tall and the rope attached to the deck 15 feet away from the base of the mast how long is the rope feet

to 50 Find the value of x in the triangle to X

Type your answers in the space provided using your keyboard and the equation editor of your word processor Write the work and answer to every question on a separate sheet of paper Take pictures of each answer and upload the picture of each answer to the appropriate answer space e sure to complete all parts of every question 1 The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 4 and 12 Find the length of the shorter leg of the right triangle 3 points X 12