2D Geometry Questions and Answers

Tools X Read the question and type your response in the box provided Your Consider this right triangle 17 30 Enter the value of side length x

Tools Question 6 Use the table below to determine the approximate height of the flag pole 35 2024 25 ft A B C 14 3 ft 17 5 ft 20 5 ft D 35 7 ft sin 35 0 57 cos 35 0 82 tan 35 0 70 Illuminate Education TM Inc 4

Tools O Question 4 Which pair of equations can be used to solve for x in A PQR P A B C D 18 Q 57 sin57 cos57 sin57 tan57 R 18 18 18 x and cos33 18 and sin33 1 18 18 x and cos33 and cos33 18

Tools A B C 6 Which trigonometric ratios are equivalent to Select TWO that apply U 10 cos P sin P cos R 8 sin R R

State whether the following measures can be side lengths of a triangle Click Yes or No for each situation A 4 4 7 B 2 9 12 C 3 5 8 D 10 12 15 Yes Yes Yes Yes No No No No

Question 9 G A B C K 6 JG 13 N M II Pause 7 ZJ 7 ZH 7 and ZG 7 ZJ 7 but not ZH or ZG Q Zoom

4 Question 7 AJKL is shown below Choose the correct option that has the angle measures from least to greatest K 6 8 cm A B C D 8 9 cm ZK ZJ ZL ZJ ZL ZK ZJ ZK ZL ZL ZK ZJ II Pause Q Zoom 2024 Illuminate Education Inc 5 2 cm L

4 H Using the information provided select the triangle congruence criterion that can BEST be used to prove that AHFGA HKJ A angle angle side AAS angle side angle ASA side angle side SAS side side angle SSA B C D C2024 Illuminate Education Inc

Which congruence postulate or theorem shows that the triangles Welow are congruent 38 15 A B 100 AA AAS ACA 100 15 380

In the figure shown PSRQ Which theorem can be used to prove ASQR AQSP P 0 00 A B C S R SAS Congruence Theorem SSS Congruence Theorem AAS Congruence Theorem

csc0 1 Cose csc 1 Multiple Simplify the following csc0 1 trigonometric expression by following the indicated direction by

19 YT 9 Find TW W X T Z

5 Triangle ABC has been dilated from center D to form triangle RST 10 7 5 R S Is AGRS AART Explain 25 A T 12 cm C If the length of the segment AC x which is the length of the segment RT Date 10 6 In the diagram below GRS ART GR 36 SR 45 AR 15 and RT 18 G 36 A 45 15 R A 10 cm 18 Alex designed a plan for a large mosaic wall including a scale model below T 9 R 1 C 88 45 30 6 20 15 25 2 25 The wall is 10 m wide and 7 m high What are the dimensions of the largest mosaic he can make on that wall Explain He will use 2 cm square tiles to make his mosaic How many tiles will he need Explain how you found your answer 316 AJA Jus

3 Write the fraction ratio for each of the following 1 point a tand b sinD c cosD 4 Ifm H 68 what is GI Round your answer to the nearest tenth 1 point 4 8 1 7 G 2 cm F

B 62 X A 8 C Optional Complete When you

Dik koordinat d zleminde birim ember a a da veri mi tir 1 1 3 olmak zere A m n noktas birim ember zerindedir Buna g re m n arp m n n de eri ka t r M n

Determine is D the two graphs are equivalent E B F 0

1 25p x A 50 cm C 70 B c the amount of change in plate thickness d the final volume of the plate 150 MPa E 70 GPa v 1 3 40 cm 1 5 cm ABC triangle is drawn on the thin plate in the figure when it is unloaded AB length is parallel to the x axis and measured as AB 20cm Determine a the final length of side BC b the amount of change of side AC 90 K MPa

3 Run of mine ore is blended using a stockpile with a conical shape see image below The stockpile has a slope angle of 39 degrees and a height equal to 20 24 m The volume of the stockpile is known to be 13 250 m 39 For calculations relating to this shape recall that the volume V of a cone follows from V R H 20 44 where V is the volume R is the radius of the base H is the height The surface area S of a cone is given by S R RL where S is the surface area R is the radius of the base L is the slant height which is measured along the sloping side a Determine the radius R of the stockpile in m to 2 decimal places b Determine the slant height L in m to 1 decimal place R c Determine the surface area S in m to 0 decimal places To increase the size of the stockpile is adjusted as follows slant height L is increased to 35 m and 0 surface area S increases to 5000 m at the same time while height H remains as before d Determine the new radius R in m to 2 decimal places e Determine the new slope angle in degrees to 1 decimal place Determine the new volume V in m to 0 decimal places 2 marks 2 marks 2 marks 3 marks 2 marks 1 mark

Complete the statement W Z Y If ZXYZZZXY then 211 Select the theorem used to find the answer O Converse of the Base Angles Theorem O Third Angles Theorem O Base Angles Theorem Trianglo S www XV D VX

D S cian ka t r E 3 D r 11 K eleri A 2 3 B 6 6 ve C 4 0 olan ABC ge ninin BC na ait kenarortay iziliyor Buna g re kenarortay do rusunun y eksenini kesti i noktan n ordinat ka t r A 2 B 1 C O B D 1 E 3

AD Rhombus Statement ABCD is a rhombus DF bisects BC ZDEC FEB ZCZEBF DC AB BE CE BF AD BF DC ADECAFEB DC AD Reorder steps to make Given it logical Vertical angles are congruent Parallel lines cut by a transversal fo Opposite sides of a rhombus are par A segment bisector divides a segmer Transitive Property Corresponding Parts of Congruent T ASA All sides of a rhombus are congruen D E C

13 AUVWALLS W by SSS UK 14 APQR ARMQ by SAS Q P T R S

15 AABE A CDE by ASA D B E C 16 AABCDEF A C B by D

13 AABC A DEA A C by D BF E 14 AABC AAD by SSS A D B C

11 AABC Azx B Z 3 AUVW AYLS C by AAS Y by SSS aining 2 co tam 12 ANRM ANG P by ASS M A R 14 APQR ARMQ by SAS P

Determine whether each set of triangles is congruent 2 points each If they are complete the congruency statement and name the triangle congruency theorem that applies and mark any implied relationships Your markings MUST match your theorem If they are not congruent cross off the figure completely 9 AEGHA GEF E H by SSS F visloxo 61 G 10 AABDARD by HL B mt no b5263 neo mengert A BA C M1 15 101

5 You are given ARST and AEFD such that m R 60 m2S 80 m2F 60 m2D 40 RS 4 and EF 4 Are the two triangles congruent If so which segment is congruent to RT nomic ross A Yes the triangles are congruent FD B Yes the triangles are congruent EDNA gnitbelter norw woled engil silf no bezsa C Yes the triangles are congruent FE D No the triangles are not congruent ZVGWIA A 29mizemcz

Length of a circular arc Length of AB 2ar A Find the length of AB Round your answer to the nearest ten 8 in 100 B Select one a 50 3 in d Ob 55 9 in OC 20 9 in 14 0 in

10 Determine the value s of k such that the area of the parallelogram formed by the vectors k 1 1 2 and b k 3 0 is 41

7 Suppose DE a DG and LEDF 2GDF Are there congruent triangles in the diagram Where do you find the corresponding congruent parts to satisfy either SSS SAS or ASA G CO B 7 A F Analyze the triangles shown G CO B 7 AY 86 810 6 A RAKAN ENABLEDES

24 Refer to Illustration 10 Given LA LB AC BC Prove AAFC ABEC A E C D B

Calculate perimeter blank 1 and area blank 2 of the following shape 1 5 cm 2 5 cm Blank 1 Blank 2 9 2 cm A

B ZB 29 15 m A C 27 75 m

Calculate the volume of the cone below look at formulas sheet or formulas above 4 2 m J 3 6 m

B a side c 16 15 00 m C C A

Calculate the volume of the cylinder illustrated below 50 cm 38 cm

Based on the following diagram and assuming that the wall and floor meet at a right angle how far up the wall does the ladder reach Top 5 feet 13 feet

the following problems using Pythagorean Theorem Round to the nearest tenth where necessary Always include units in your answer For example if you answer is 100 feet write 100ft Question 6 2 points Listen If a rectangular soccer field has length of 240 meters and width of 70 meters How long is its diagonal D 70 m 240 m

x a 5 x 6 7 x fonksiyon ise f 2 a b bir sab f x fonksiyonunu bulunur

Find the value of y K Fro 28 H

Find the circumcenter of the triangle 15 10 86

Use the figure at the right If JK 7x 16 and NO 15 what is the value of x N HE L M K

In ADEF the midpoint of the side opposite vertex D is M and the centroid is C If DM is 21 what are DC and CM DC 14 units CM 7 units

solving the triangle A ZA LB ZC b 31 586 38 942 degrees degrees degrees C a 5 b 6 C 9

11 67 A ngle C measures 67 and AC has length 11 find Angle B in degrees 23 The length of AB The length of BC B ou use a calculator to find a decimal approximation your answer must be accurate to at least 3 imal places st be sure that your calculator is set to degrees not radians

8 220 AM

b x 56 67 67

5 Find an equation that gives all points P x y such that the absolute value of the differences of the distances of P to 1 3 and 1 9 is always 4 Your answer should be a b 1 j k where a b j and k are constants in the form

9 130