2D Geometry Questions and Answers

What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate B C D OA AC BD OB ZBAC ZDAC OC ZCBA CDA OD AC1 BD

4 A triangular plot of land has three sides one measures 110 feet and another measures 215 feet The angle between these two sides is 65 a Draw a rough sketch of this plot of land You do not need to measure this sketch but you should try to make the 215 foot side about twice as long as the 110 foot side Also try to make the angle close to 65 b Decide on a scale Look at your longest measurement Try to make your drawing fill about half a page Write the scale in a box on your drawing Note If you are having trouble deciding on a scale read example 1 c Convert all the real measurements using your scale d Use a ruler and protractor to make a scale drawing Label all sides with their ruler measurements and in parentheses the real world measurements Label angle measurements as well e Measure the third side of the triangle in your scale drawing How long is the third side of the lot

Andrew is proving that AJKL AMNO given LKJL ZNMO and ZKLJ ZNOM He has already MO determined that a dilation with scale factor JL will map AJKL onto AJ K L where J L MO Which congruence criterion should Andrew use to show that AJ K L AMNO SSS SAS ASA M AAS

State if the pair of triangles are similar If so state how you know they are similar and complete the similarity statement 828 804 Q 1120 not similar AQRS 1151 similar SAS similarity ACDQ similar AA similarity ACDQ similar SSS similarity ACDO R

Calculate the volume of an object with dimensions measuring 12 cm x 3 cm x 9 cm 21cm3

M A P N In Rhombus LMNO angle LMN measures 31 20 degrees what is the measure of angle MNO Type your answer

The diagonal of a square is 381 What is the length of a side

Solve For Angle A B 11 9 7 10 10

The total cost of being a member of Grenoble Soccer Club is represented by y 20x 150 where y is the Total Cost for club membership and x is the months you have been at the club Call this equation Line 1 The total cost of being a member of East York Soccer Club is represented by y 30x 100 where y is the Total Cost S for club membership and x is the months you have been at the club Call this equation Line 2 190 180 300 290 280 270 260 250 240 230 220 210 200 170 160 150 140 130 10 20 120 110 100 90 80 70 60 50 40 30 20 10 Find the point of intersection of the lines Use one method to solve Option A Solve this Linear System by graphing Graph the two equations on one grid one graph with two lines Label each axis Label the intersection point on the graph

the angle of elevation theta of the sun and sky at any latitude L is calcuclated with the formula sin theta cos d cos I cos w sin D sin L W is the number of raidans the earth has roated through since noon when W 0 D is the declination of the sun westville has a latitude of 35 8 degrees find the angle of elevation theta in degrees of the sun at 3pm on febuary 29 2012 Where at that tine D 0 1425 and w 0 7854

Match the notation with the term that best describes it D HF ZBAD AB G LFGE AB AD E F E 1 Radius 2 Diameter 3 Secant 4 Chord 5 Tangent 6 Center 7 Point of tangency 8 Central Angle 9 Inscribed Angle

What is the name of a segment that has both endpoints on the circle and contains the center of the circle

The quadratic parent function is f x x 2 Its gra its vertex at the origin 0 0 Describe each tran parent function 2 g x x 2 g x

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