2D Geometry Questions and Answers

For the following right triangle find the side length x Round your answer to the nearest hundredth 11 X 9 0

1 Find x if m NMY x 10 m NML 17x and m YML 150

Identify the parts of the circle below Figure 1 use proper geometric naming schemes 1 Segment CA 2 Segment AD 3 Segment BH 4 Segment BG 5 Segment GH 6 Segment GE 7 Point F Figure 1

X 6 mZX O N 4 Write your answer as an integer or as a decimal rounded to the nearest te Y

Name the transformations g x f 1 x 8

Solve the right triangle H 2 43 HI mZH MZJ 43 Write your answers in simplified rationalized form Do not round 0 0 J

E F 3 mZE 8 Write your answer as an integer or as a decimal rounded to the nearest ter O G

Solve the right triangle C BC m C MLA 2 7 Write your answers in simplified rationalized form Do not roun 00 O B O A

The entire rectangle below has an area of 28 in Find the area of the shaded triangle Be sure to include the correct unit in your answer

Find the area of the right triangle 1 unit O Area 0

Find the area of the right triangle Be sure to include the correct unit in your answer 20 cm 29 cm

ren 0 In the figure m22 92 and m212 74 Find the measure of each angle 1 210 42 92 3 29 5 211 106 248 92 m2 74 4 25 106 6 213 106 74 X13404

4 3 4 1 1 2 2 4 2 1 4 1 1 2 2 4 4 3 2 1 N y 1 2 y f x 3 4 Use the above graph of a function f to answer the following questions a 2 points each For each of the following intervals indicate whether or not f x satisfies the hypotheses of the Mean Value Theorem If not indicate which con ditions are not satisfied X b 2 points each For each of the following intervals indicate whether or not f x satisfies the conclusion of the Mean Value Theorem If the conclusion is satisfied indicate the value e at which it is satisfied

Choose ALL answers that describe the quadrilateral VWXY if VW XY WX YV diagonal VX 19 and diagonal WY 19 Parallelogram Rectangle Rhombus Square Trapezoid

Weight pounds 8 7 6 4 3 2 1 1 2 0 84 pounds per week 3 4 pounds per week 3 4 5 6 Time weeks Which is the best estimate for the pumpkin s average growth rate 1 7 pounds per week 7 6 8 pounds per week 8

Fred repairs and sells used cars He made this table to show the approximate value of a mid size car over time Age years 3 4 Value 16 500 14 400 12 700 11 100 9 500 Complete the sentence to describe the average rate of change shown in the table 5 6 7 The car s value decreases increases by about per year

DID YOU LABEL YOUR TRIANGLE OPP ADJ AND HYP DID YOU WRITE OUT YOUR TRIG EQUATION DID YOU CIRCLE YOUR ANSWER Solve for x 40 12

Triangle ABC is graphed in the coordinate plane with vertices A 1 1 B 3 4 and C 1 8 as shown in the figure 9 C 1 8 8 5 4 1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 6 7 8 B 3 4 A 1 1 1 2 3 4 5 6 7 8 9 Part B What are the coordinates of B After a Enter your answers in the boxes anslation of x y 6 X

A a 1 b D 5 2 A 5 B a 3 4 ekilde ABCD paralelkenar A a 1 b B a 3 4 C k 7 D 5 2 oldu una g re b k ka t r B 6 C K 7 C 7 D 8 E 9

ekilde ABC gen AD a ortay 4 IABI 3 IACI B 0 4 C 7 3 oldu una g re D noktas n n koordinatlar arp n ka t r B 0 4 A J D C C 7 3 2 C C

select the reasoning for your answer M 25 Answer 1 similar 14 L The figures are similar because the corresponding angles are congruent and the corresponding sides are proportional A VUT AVLM Answer 2 This is correct However we are using the following criteria 8 V All sets of corresponding angles are congruent All sets of corresponding sides are proportional congruent 49 28 As we do not know all three sides of each triangle and have no way of calculating the missing side We don t have enough information to determine if all three corresponding sides are proportional We would need to use similarity postulates which will be covered in the next section U Answer 3 Using the following two theorems we can calculate all angles in the given triangles proportional Answer 4 VLM Vertical Angles Any pairs of opposite angles made by two intersecting lines are always congruent Triangle Angle Sum All three angles in a triangle will always sum to 180 degrees 25 The following properties occur if two figures are similar All sets of corresponding angles are congruent T

Determine if the following figures are similar and also select the reasoning for your answer 84 59 48 Answer 1 similar Answer 2 A CBA AGFH 33 Answer 3 88 congruent Answer 4 GFH 72 12 proportional B H The figures are similar because the corresponding angles are congruent and the corresponding sides are proportional G 33 88 14 59 8 F The order of the letters matters Match corresponding vertices they should be in the same location first letter second letter third letter The following properties occur if two figures are similar All sets of corresponding angles are congruent

If two figures are similar what must be true about their corresponding side lengths Proportional Congruent Similar

EFGH is a parallelogram whose diagonals intersect at point B Some of the measurements are shown Draw EH 4x18 34 GB 0 6x 23 5 0 6x12B FH 352 G 4X 34 Set up an equation that can be used to determine the value of x Find EF Equation BAGY A X BH 5x 6 2 GH 4x 34 352 EF

Given the information below determine the value of x S X 70 D T 11x 4 B 50 60 C R ASRT ACBD

Find the rule to describe the transformation E 5 3 F 5 1 G 1 2 E 2 5 1 5 F 2 5 0 5 G 0 5 1 O Dilation of 0 5 O Dilation of 3 O Dilation of 0 25 O Dilation of 1 25 None of the other answers are correct

Use cross products to solve for x Type your answer as a simplified fraction Ex 37 4 3x 8 6 X 2x 10

Simplify the given ratio Write your answer as a fraction with no units meters

Bob is playing a basketball game at an arcade He needs to make as many baskets as possible in one minute This table shows his score over time Time seconds Total points 0 12 24 36 48 60 0 4 9 15 19 25 Complete the sentence Round your answer to the nearest tenth Bob s score increased by an average of Submit points per second during the game

Statements Reasons 1 1 m 2 21 23 3 1 l 2 4 42 43 Select Transitive Property Given Vertical Angles Theorem Corresponding Angles Postulate Select 4 Select

Alternate Interior Angles Theorem Given m Prove 22 23 Statements Reasons 1 7 m 2 41 43 3 1 2 4 42 43 1 2 Select Select Select Verttical Angles Theorem Given Transitive Property Corresponding Angles Postulate 2

Find the value of x Only type a number in the box no spaces X 21x B 13x 24

10x 55 X 45 Type of Angles Given Select Select

Identify the missing angle that completes the description 7 7 3 5 6 8 m23 Select m23 Select m27 Select m26 Select 1 4 2 m by the Alternate Interior Angles Theorem by the Corresponding Angles Theorem b by the Alternate Exterior Angles Theorem 180 by the Same Side Interior Angles Theorem

Use the equation editor to write the equation for the function described Type of function Exponential Parent function f x 5x Horizontal Shift left 2 spaces Vertical Shift up 4 spaces

1 200 6 300 Find the Average Rate of Change for the given interval 1 x 6 The average rate of change is 100 V

10 a Part A Consider the function f whose graph is shown below f x b 3 2 The domain of the function is A 6 x 4 B 10 x 8 C 9 x 7 D 9 x 6 Part B 8 7 6 5 4 3 2 1 The range of the function is L 2345 6 7 8 9 2 f x

Determine whether a triangle with the given side lengths is a right triangle Side lengths 10 26 28 10 11 15 16 30 34 5 12 13 Right triangle Not a right triangle X Not enough information

A 12 ft ladder leans against the side of a house The bottom of the ladder is 6 ft from the side of the house If necessary round your answer to the nearest tenth al 12 6 ft

Given W 2x 5 What is the value of x Keypad Z X Y 4x 25

A sequence of transformations maps triangle ABC onto triangle A B C as shown in the figure below State the composition mapping triangle ABC onto triangle A B C B B A C A C V A B C

8 The coordinates of A ALT are A 5 1 L 3 2 and T 3 2 a Rotate A ALT 180 then translate the image by the rule x y x 3 y 2 Give the coordinates for each image od el S b Write the composition rule mapping A ALT onto AA L T m ct RD 3 T r T T A C L T 100

C Assuming m VUX 56 and measure of arc VX is 76 determine the measure of an L

R 5 S 59 ST T Write your answer as an integer or as a decimal rounded to the nearest te

T U 63 8 V Write your answer as an integer or as a decimal rounded to the nearest tem TU

Graph the two equations f x 0 1x 2 0 5 g x 0 1x 3 4x and find the volume if the cross sections perpendicular to the x axis that are equilateral triangles

Find GI I 26 GI G 61 H Write your answer as an integer or as a decimal rounded to the nearest ter

Choose all of the statements that correctly define the geometric term A Lines that never intersect or cross each other perpendicular B A circle is the locus of all points in a plane that are a fixed distance from a given center point C D Two rays joined at the same end point form an angle A continuous section of the circumference of a circle is a circular arc

Which statements can be used to describe a ray A Has only one endpoint B Has no dimension C Extends endlessly in both directions D A part of a line E Has two endpoints

Defined by distinct lines which intersect at right angles and at exactly one point A perpendicular lines B C D arc angle parallel lines