2D Geometry Questions and Answers

of 2 1 Book Hint Print erences Required information The following information applies to the questions displayed below Hudson Company reports the following contribution margin income statement HUDSON COMPANY Contribution Margin Income Statement For Year Ended December 31 Sales 10 000 units at 300 each Variable costs 10 000 units at 240 each Contribution margin Fixed costs Income 1 Compute break even point in units 2 Compute break even point in sales dollars 1 Break even units 2 Break even sales dollars units 3 000 000 2 400 000 600 000 420 000 180 000

TAN In 4 21 Find the length of the missing side x using sine cosine or tangent ratios MUST SHOW YOUR WORK 10 4 50 20 7 26 A 24 X 11 50 5 8 29 12 X 34 17 6 9 20 X KERAVANORIME X 54 8 11 12 4 4 15 25 34 65

In 1 5 Use the given figure to the right for which line a and line b are cut by transversal line m to name each of the following 1 All four pairs of Corresponding Angles 2 Both pairs of Alternate Interior Angles 3 Both pairs of Same Side Interior Angles 4 A pair of Vertical Angles 5 A Linear Pair 5 1 6 2 3 7 In 6 10 use the figure below for which lines and line w are cut by the transversal line t to name each of the following 6 All four pairs of Corresponding Angles 7 Both pairs of Alternate Interior Angles 8 Both pairs of Same Side Interior Angles 9 A pair of Vertical Angles 10 A Linear Pair W 4 7 8 8 4 1 3 2 6 5 a b

Use a trig ratio to approximate the measure of the given angle to the nearest degree 6 4 ZB 7 P a 8 0 B Went to the leag Solve the right triangle Round decimal answers to the nearest tenth Find the length of all missing sides and the measure of all the missing angles Round to the nearest tenth 22 37 5 R 0 ZR 8 Q 18 Ishodh 11 N 2T 9 14 L 51 M D

4 F Find the missing sides of each triangle 1 6 G 15 G H 60 F H FG 60 FG GH GH SC 60 G FG H 4 3 FH AG 7 A 5 8 B 2 B R 11 T SON S 5 2 45 C 15 14 H D AD BD F 60 H FG FH BH CH to abi 3 R 103 T 6 A 12 F C 10 5 2 D RT TS DC D AD CA AD GUITTAL BITT

Question 7 Find the distance between P 4 8 and Q 5 5 O A O B C 18 34 170 D 10

K Find the exact value of the expression tan arcsin lon 19 6 1 75 O Points 0 of 1 tan arcsin Type an exact answer using ra

Use a calculator to find the value in decimal degrees tan 0 1051 tan 0 1051 Round to four decimal places as needed

Verify the identity 2 tan 0 2 2 tan 0 1 tan 0 2 tan 0 2 tan 1 2 2 tan 0 tan 0

A flagpole at a right angle to the horizontal is located on a slope that makes an angle of 13 with the horizontal The flagpole casts a 14 meter shadow up the slope when the angle of elevation from tip of the shadow to the sun is 22 a Draw a triangle to represent the situation Show the known quantities on the triangle and use the variable h to indicate the height of the flagpole b Write an equation involving the unknown quantity h h 14 1 sin e Find the height of the flagpole Round your answer to two decimal places h m sin

Q is the midpoint of the line segment PR in the truss rafter shown in the figure What are the lengths of the line segments PQ QS and RS Letx 10 and y 12 Round your answer to o place QS RS

A triangular parcel of ground has sides of length 750 feet 635 feet and 585 feet Find the measure of the largest angle Round your answer to one decimal place X

cot 0 3 3 0 O Type your answer in degrees Use a comma to separate answers as needed

as the measure of 0 in degrees 3 2 cos 0 Express as an inverse trigonometric function 0 Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression

Find an equation for the indicated part of the hyperbola Lower branch of 2 2 2 2 1 25 36

Prove AABC ACDA B D Given PT RT QT ST Prove APQT ARST C X C Given C is the midpoint of AE and BD Prove AABC AEDC D E Statements Statements Statements Reasons Reasons Reasons

For 2 and 3 identify all pairs of congruent corresponding parts Then write a congruence statement for the polygons 2 Corresponding Angles Corresponding Sides Congruence Statement 3 Corresponding Angles Congruence Statement 5 m M A For 8 and 9 find the values of x and y 8 ABCDEFGH 28 B 135 For 4 7 complete each statement with the correct number value given that AXYZ AMNL 4 MzY 6 mzZ 4y 4 C Corresponding Sides 7 XY D H y G 10x 65 F A N B H 142 33 9 AMNP ATUS and same L C 12 S 2x y m M 24 y R 124 Z P N 8 13 m M E 2x

K a ZLJK LLMK b mzJLM 90 c mzLKM 90 d mzLMK 90 e LJ LK f JK MK M Name 18 D EG LL a ZDFEZHGI b ZD ZH c DF HG d DE HG e DE HI f DF HG H

10 WX LV 11 WX VWXYZ Y By the 16 N LX AWXY For 12 and 13 find m21 12 L 70 N R that the polygons are congruent by filling in the blanks XY YZ VZ WV ZW XY ZU LXYW M T LX Y W LY 14 If AJKL is congruent to AXYZ then identify all pairs of congruent corresponding parts 2 LK LLE JK property WY WY LXWY 13 c ZZ ZW LZ a ZP ZR c PQ RS For 15 18 what can you conclude from the diagram Circle all correct answers may have more than 1 answer 15 X a ZX ZV b XZ VW V KL B 80 AY 45 d ZY WU W b ZN LT W d NQ ST X JL R M Y 2

a JK and KL d LP and LK a AABD ACDB B c AYXZ AWXZ W X the pair of sides given 3 Write a proof Given PQ bisects LSPT SP TP Prove ASPQ ATPQ b PK and LK e KP and PL 2 Decide whether enough information is given to prove that the triangles are congruent using SAS Congruence Theorem Explain b ALMN ANQP c KL and JL f JL and JK Statements by SAS K G N M d AEFH AGHF P Reasons

Type the correct answer in the box 2 2 Polygon 22 20 18 16 14 12 10 B 8 U 6 4 2 24 E W The figure shows five polygons ABCDE FGHIJ KLMNO PQRST and UVWXY H R 8 10 12 14 16 18 20 22 24 26 Reset cannot be mapped onto the others by similarity transformations X Next

Select the correct answer What is the total number of lines of symmetry for this figure X OA 0 OB 1 O C OD 4 2

Use the sum to product formulas to write the sum as a product 4 cos 6x 4 cos 2x

Select the correct answer Given AD BC Prove DC 6 units A 6 units D Statements AD BC ZDAC AC AC ZDCA C ZBAC DC BA DC BA DC 6 units Which step is missing given ZBCA alternate interior angles theorem reflexive property of congruence alternate interior angles theorem B O A ADAC O B ADCA O c ADCA O D ADAC Reasons CPCTC definition of congruent sides substitution property of equality ABCA by SAS ABCA by ASA ABCA by SAS ABCA by ASA

In quadrilateral ABCD ZABC is a right angle and AB 4 units Quadrilateral ABCD is dilated by a scale factor of 2 with point B as the center of dilation resulting in the image quadrilateral A B C D Which statement is true A A B is 6 units long and lies on the same line as AB OB A B is 8 units long and lies on the same line as AB OC A B is 6 units long but lies on a different line than AB OD A B is 8 units long but lies on a different line than AB

10 A VWX and A NOP are similar If mV 44 and mP 66 what is mW OA 22 OB 33 OC 35 O D 70

6 1 Score 2 67 46 0 21 answered Question 6 Use the given figure to answer the following The figure is not drawn to scale C a B A Find B if B 75 B D Question Help Post to forum B

s Show 12 35 using an area region model

Find all solutions if 0 0 360 Separate your answers with commas and do not degree symbols sin 30 0 3 2

Given ZA ZEBC and AB BC Prove BE AC Note quadrilateral properties are not permitted in this proof Step 1 try Statement ZA ZEBC AB BC Type of Statement Reason Given B D E

Simplify the following expression as much as possible tan cot x tan x O tan x cot x 9T 2 X

Find the values of the trigonometric functions of t if cos t 3 and the terminal point of t is in quadrant III 5 sin t O sin t 4 5 sin t cos t 4 5 4 5 3 5 3 BR tan t E 5 cos t cos t EL 4 tan t cot t 3 3 5 tan t 4 3 4 cot t 4 3 cot t 3 4 3 4

The graph shows how the path of a stream of water changes when the hose is held at two different angles Scale 1 unit 1 f Nozzle beld at 60 angle Nozzle held at 30 angle 6 5 4 3 2 1 1 2 3 4 5 6 7 a At which angle does the stream of water shoot up higher 60 How much higher X ft b At which angle does the stream of water shoot out farther 30 How much farther x ft

In 17 18 Find the value then find the measure of each angle 17 7x 12 R 101 12 T 3x 28 S 18 In 19 Use a two column proof to find the value of the variable Justify each statement 19 m RST 10x 12 and m USV 32 x 32 X 3x 75 Statement m RST 10x 12 and m USV 32 x Reason Given

Find the exterior angles of the double triangle 30

In 16 Use a two column proof to find the value of the variable Justify each statement 16 m VST 11x and m RST 50 x R T S U Statement m VST 11x and m RST 50 x Reason Given

In 14 15 Find the value of the variable then find the measure of each angle 14 15 15x2 9x 10 154 3x 7

Question Watch Video Answer Attempt 1 out of 2 Show Examples From a hot air balloon Ian measures a 30 angle of depression to a landmark that s 1250 feet away measuring horizontally What s the balloon s vertical distance above the ground Round your answer to the nearest tenth of a foot if necessary G

uestion Watch Video Answer Attempt 1 out of 2 Show Example he angle of elevation to a nearby tree from a point on the ground is measured to be 74 How tall is the tree if the point on the groun 4 feet from the bottom of the tree Round your answer to the nearest tenth of a foot if necessary

Question Solve for 2 Round to the nearest tenth if necessary x 1 94 72 J

uestion Express tan K as a fraction in simplest terms L 47 M 17 K

Find the measure of the indicated angle 1 A This is the only question in this section Question Find m A Answer Attempt 1 out of 2 A

7 In 5 8 Find the value of the variable then find the measure of each angle 5 1 4z 10 32 10y 52 6 8 4x 1 7x 3 7 9x 4 113

Statement ZMON 4x 17 and m2QOP 67 Reason Given

In 1 3 Use the given figure and write a two column proof to find the value of the variable justify each step 1 NIH 10x 5and m2MJK 3x 30 Reason Given Statement m NJH 10x 5 and m MJK 3x 30

N 2 mZMON 4x 17 and mZQOP 67 M M 3 m AEC 23x 83 and m DEB 5 12x 5z 9 D E K B In 4 5 Find the value of the variable then find the measure of each angle 4 8z Statement mZMON 4x 17 and m QOP 67 Statement mZAEC 23x 83 and mZDEB 5 12x 5 4x 1 65 Reason Given Reason Given

The figure shown is a rhombus HJ has length 6 FG has length 10 Find the length of FJ E H 6 J I

8 Graph the equations below to form the figure Label the coordinates of the vertices 1 y x 2 y 3x 9 3 y 2 x 4 y 5 10 10 5 10 4 points 10 4 points

6 Plot Figure ABCD given the points A 1 3 B 1 8 C 3 3 and D 1 2 10 S 10 10 Loid 4 points O on TBS HAW Ame d What is the most precise name for this figure 10 a How many sets of parallel sides does the figure have Show calculations to justify your answer 1 point b How many right angles does the figure have Show calculations to justify your answer 1 point c Does the figure have 4 congruent sides Show calculations to justify your answer Irbe 2 points 2 points

2x 3y 4 and passes through the point 1 3 ay 3 x 1 by 3 x 1 y 3 x 1 d y 3 x 1 2 3 4 b c y x d y 5x 17 Which equation represents a line parallel to the y axis x 5 y 10 Which statement is true 2x Points A 5 3 and B 7 6 lie on AB Points C 7 6 and D 1 10 lie on CD a AB CD b AB 1 CD c AB CD are the same line d AB CD intersect but are not perpendicular c AB CD d Not enough information is given 3y 2x 4 33 Using the same information from the problem above which statement is true about the length of the segments a AB CD b AB CD 5 Below the equations of lines A B and C are given Determine whether each statement is true or false Line A y x 2 AIC WAS ALB Line B y 6 x 7 1 point each Line C 4x 5y 5