2D Geometry Questions and Answers

Show your work here ZF 4H 49 The triangles not congruent EF EG 49 F The triangles are congruent by the AAS criterion ZGEF LEGH because they are alternate interior angles G

Identify the expressions equivalent to cos 46 given the triangle Please select two Show your work here U sin 44 sin 46 cos 136 m 29 5 8 46 4

Which expressions represent the length of b Please select two Show your work here 3 2 sin 76 3 2 sin 14 3 2 sin 14 3 2 sin 76 3 2 cos 76 b 76 3 2

Which expressions represent the length of m Please select two Show your work here cos 59 66 sin 59 66 sin 31 66 sin 31 66 m 59

Identify the expressions equivalent to cos 62 given the triangle Please select two Show your work here sin 62 cos 152 51 24 62

Select the true statement in rere 25 7 Show your work here fice to the triangles 67 19 46 13 The top triangle is similar to the bottom with a scale factor of 2 1 The top triangle is similar to the bottom with a scale factor of 3 5 1 O The top triangle is similar to the bottom with a scale factor of 3 1 O The top triangle is similar to the bottom with a scale factor of 5 1

Use a trigonometric ratio to solve for z Round to two decimal places as necessary 16 Show your work here Z 12

ind the amplitude period and f x 4cos x 2 1

equation for the axis of sym g x x 3 2 3

You are given the parametric equations 2 cos 0 y sin 20 a List all of the points x y where the tangent line is horizontal In entering your answer list the points starting with the smallest value of x If two or more points share the same value of x list those points starting with the smallest value of y If any blanks are unused type an upper case N in them Point 1 x y Point 2 x y Point 3 x y Point 4 x y Point 5 x y Point 6 x y b List all of the points x y where the tangent line is vertical In entering your answer list the points starting with the smallest value of x If two or more points share the same value of a list those points starting with the smallest value of y If any blanks are unused type an upper case N in them Point 1 x y Point 2 x y Point 3 x y Point 4 x y Point 5 x y

A semi elliptical window is 44 inches wide and 15 inches tall Determine the height of the window 19 inches from the center Height of window inches Enter your answer correct to 3 decimal places

A 1 2 1 2 and 8 1 2 1 B 2 The points A are two points on the unit circle If the point 0 0 0 is the centre of the unit circle then the measure of the smallest angle AOB can be expressed in the form a a where is a fraction in lowest terms Enter the b values for a and b respectively as ab Do not include spaces or commas

7 Your friend says you ca convince your friend that 11 cm

y 6 5 4 3 2 1 4 3 2 1 0 1 2 3 4 A f x 2 B f x 2 1 C f x 2 1 D f x 2 2 X The graph of y f x 1 is shown Which equation could define function f

Find the length of segment CA A D 3 3x 12 L 14 4x 1 B

The diameter of a circle is 12 inches What is the circle s area Use 3 14 for

ath Language arts rade Y 6 Area of circles YA8 Recommendations The radius of a circle is 2 meters What is the circle s area r 2 m

Find the vertices the endpoints of the minor axis and the foci of the given ellipse 16x 128x 5y 10y 181 0

A 48 mm B 81 mm C 68 mm and a 21 mm Then find the perimeter and area of BOTH triangles Use proportions to find your answers and round to the nearest whole number if necessary A B

64 Check in Cakulate the length of each line segment in the problems below The length is Name The length is Block

9 Solve for x and use x to find the value of mAB MGSE9 12 G C 2 B A 2x 5 17 a x 11 mAB 34 b x 25 5 mAB 46 C D LC 2x 5 LD 17 C x 17 mAB 46 d x 11 mAB 17

How do you use theorems about triangles to solve problems EXTRA PRACTICE for 2 03 2 06

prob 12 5 pts Graph the following data and determine the order and rate consta k Find lineur 0 vs 1st vs 2nd Time s Concentration M 0 5 10 15 20 25 30 35 to find 2 50 1 92 1 55 1 31 1 13 0 992 0 887 0 799

Find the distance between each pair of points 11 2 8 5 4

State if each triangle is a right triangle 9 41 ft 5 ft 4 ft

In Figure 6 1 the consumer surplus is equal to AJ 400 B 300 C 200 D 100 24 If the good in Figure 6 1 were free A consumer surplus would equal 450 and consumer expenditure would be 50 B consumer surplus and consumer expenditure would both be maximized C consumer surplus and consumer expenditure would both be zero D consumer surplus would be maximized but consumer expenditure would be impossible to calculate 25 As price falls along a particular demand curve consumer surplus A decreases rapidly B decreases by a very small amount C remains constant D increases 26 A market equilibrium will generate the largest possible surplus when A there are no external benefits and external costs B there is perfect competition C perfect information is available D all of the above 27 Buyers and sellers acting in their own best interest generate outcomes that are in society s best in when all of the following are true EXCEPT A buyers and sellers are informed B markets are efficient C there are no external benefits D there are no external costs AC AC

7 Determine if each relationship is a proportional or nonproportional situation Explain your reasoning Assume that the tables represent linear relationships 3 t 15d 5 y x X 10 8 6 4 2 2 O 5 12 Practice and Problem 2 4 y 11 26 61 6 8 10 2 101 8 8 6 4 2 O 2 4 m 0 75d 2 6 r b 1 4 6 8 10 X 4 10 13 y 36 90 117

The radius of a cone can be found using the formular 3V where V stands for the th volume of the cone and h stands for the height Ifr 4 h 8 and is 3 14 find the volume V Round the answer to the nearest hundredths place O3 365 41 cubic units O 133 97 cubic units O 66 99 cubic units O 33 49 cubic units

A student wants to know how far above the ground the top of a leaning flagpole is At high noon when the sun is almost directly overhead the shadow cast by the pole is 10 ft long The student holds a plumb bob with a string 2 ft long up to the flagpole and determines that the point of the plumb bob touches the ground 13 in from the base of the flagpole How far above the ground is the top of the pole 12 ft 13 in 10 ft

22 A triangle has the base and height show x 12 X 4 What is the area of the triangle

24 What is the simplified radical form of the expression x 3 7

12 Write 8x2 With rational exponents A 8x B 8 x 813 x D2 x3 Nal a None of the answer choices are correct

18 Which statement is true about the polynomial equation 4x2 2x 8 0 A This equation has exactly two zeros and both are real numbers B This equation has exactly two zeros and both are complex numbers C This equation has exactly one zero which is a real number D This equation has exactly one zero which is a complex number

17 Simplify 2 5 4 2 7 3 A 6 7 9 8 B 8 10 14 15 4 20 6 35 D10 8 10 21

13 What is the inverse of the function y 4x 5 1 5 4 5 4 A X B y 1 DY 4 X y 4x 5 1 4x 5

Graph the parabola do not place any dots then fill in the blanks about the vertex any intercepts the domain and range Enter intercepts as ordered pairs aka points y z 2z Clear All Draw Vertex 4 y intercept z intercepts Domain So 10 9 to h 8 7 6 104 5 4 10 9 8 7 6 5 4 3 2 1 1 3 2 the t 1 251 4 6 7 8 9 104 1 2 3 4 5 6 7 8 9 10 Range Equation of the Axis of Symmetry

10 If FH and EG are diameters of OP Find the following arc measures Show your work mEF mFG mDFG Challenge 1 What is mCB 65 A D B 2x 19 3x 4 Rand mDE m DHG mDGE 12 Solve for x A E D ROR FL showny wor B P 5x 10 H 38 G d

In circle D with m CDE 96 and CD 4 units find the length of arc CE Round to the nearest hundredth D E

In circle T with m STU 78 and ST 8 units find the length of arc SU Roun to the nearest hundredth T S U

Identify the expressions equivalent to cos 53 given the triangle Please select two Show your work here sin 53 60213 22 10 sin 37 10 53 6

Find the measure of angle z in degrees Round to two decimal places as necessary Show your work here 32 22 Z

B Name the inscribed angle and its intercepted arc What is the measurement of the arc if the inscribed angle is 48 What is the measurement of the inscribed angle if the interceptec arc is 112 C A

10 If0 e 90 and cos 9 25 A B 6 6

A guy wire is attached to a pole for support If the angle of elevation to the pole is 67 and the wire is attached to the ground at a point 137 feet from the base of the pole what is the length of the guy wire round to 2 decimal places A 148 83 feet B 350 62 feet C 58 15 feet D 143 40 feet E 578 29 feet

2 A B tan D tan D tan D tan D 24 30 18 24 Given that AABC is similar to ADEF which is a possible trigonometric ratio for D 24 18 3 30 01 A B 4 5 C D E F

17 The graph below is a transformation of the parent function p x x What function is shown in this graph V A g x x 2 B g x x 2 3 C g x 2 x 3 D g x x 3 2

Which of the following graphs represent the function f x x 4 and the graph of its inverse O O 4 3 2 2 3 4 5 2 3 41 5 4 3 2 1 3 ir Wi 10 4 3 T 2 3 5 5432 AY 41 23 4 5 x

For which pair of triangles would you use ASA to

You know the following information about triangle ABC a What additional information is needed to prove that the 12 ZBE ZE

On your geometry test you have two triangles