Geometry Questions

b Solve the triangle by finding the length of DF and the measures of all the angles For side lengths round to the nearest tenth For angles round to the nearest degree 2 points a DF LE 2F 7 Find all the missing side lengths for the following triangles 3 points 2 V U 30 5 3 2 60 b 2 2 d b D F 45 a 5 ft E 5 83 ft 7 4 m 45 n

Learning Goal I can solve right triangle problems using trigonometric ratios and the Pythagorean Theorem Standard G SRT 8 EXPLORE Area of Triangles Read Explore passage and complete the activity below Show all your work Example To find the area of a triangle use the following 7 7 km 14 m lem Solving with Trigonometry Area 1 base x height 2 Find the area of the following triangles 8 m 20 7m A bh 16 m 19 km 11 km 1 L4L Student Resource Center http Bit ly LALMath 16 yd 6 yd 11 yd

Trigonometry ASSESSMENT Credit Checkpoint Complete the following problems Show all your work Round all side lengths to the nearest tenth and all degrees to the nearest degree When applicable leave your answers in radical form How I Did Circle one I got it Learning Goal from Lesson 13 1 and 13 2 I can explain how to derive the trigonometric ratios for acute angles 1 Name the following sides of the triangle 1 point a Opposite Leg of ZA b Adjacent Leg to ZA bu A N B 2 Write an equation that can be used to find mzM Then solve it Round to the nearest degree 1 point 5 I m still learning it 11 M

HW 2 1 What values of u and v are correct for the following 45 45 90 right triangle 10 A u 45 D u B C u 10 2 10 6 10 6 v 10 3 u 10 2 v 10 2 v 10 v 10 45 X 11 3 3 Find the missing side lengths Leave your answers as radicals in simplest form m work Complete problems 1 6 below for independent practice 14 When you are finished check the solutions with your teacher 5 Find the missing side lengths Leave your answers as radicals in simplest form 60 y 2 What values of a and b are correct for the following 30 60 90 right triangle 30 A a 34 b 17 3 B a 17 3 b 34 68 3 C a 3 D a 34 b 17 6 4 Find the missing side lengths Leave your answers as radicals in simplest form 16 45 16 17 6 Find the missing side lengths Leave your answers as radicals in simplest form y 30 b 17 6 Optional Complete problems 3 10 18 22 your textbook on separate lined paper

Your Turn Jhangos 1 Find the unknown side lengths and trigonometric ratios for the 45 angles a Find CA b Find AB c Complete the table Angle 45 sinx opp hyp COST adj hyp B 45 tant opp adj 10

1 mzY Love 2 mzz lifelong LEARNING to the nearest degree Geometry A alla staminoghT 23 AOTHAOHO2 14 Credit 5 ZL4L Geometry A 2020 Page 123

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

7 Solve for x B 18 1 62 B X 52 9 Solve for x C 8 5 C A 8 Solve for x A 56 A 18 10 Solve for x 33 C C 7 B EVALUAT Learning I ca

7 Throughout this question leave all answers as exact expressions in terms of it and 2n square roots for example 2 n 3 or etc In the diagram below the circle centred at O has radius 3cm The curved line AOC is part of a circle also of radius 3cm centred at D OD is perpendicular to AC a Calculate the length AB DIAGRAM 1 b Calculate the area of triangle AOC A B D c Calculate the area of sector OADC in diagram 1 indicated for refere 2 below DIAGRAM 2 B A d Calculate the shaded area indicated in diagram 1 D 1

4 Let 0 A B and C be the vertices of a tetrahedron and 2 1 2 is the centroid of OABC by ratio 3 1 Vertex O is the origin If G is a centroid of AABC for the tetrahedron evaluate the value of 1OG 1

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

12 x ka t r What is x A 13 y D 16 X 12 ekilde verilen 5x5 lik kareye 1 den 25 e kadar say lar birer kez kullan larak yerle tirildi inde her sat r ve s tu nun top The total of every row and column is equal when the numbers to 25 from 1 are placed into 5x5 square in the figure given by used once N B 14 E 17 C 15

A 8 B 60 LO 5 D X E 7 x

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

Complete the two column proof 5 points Given BD bisects LB ZA LC Prove AABD ACBD BD bis ects CB LA ELO ABD ACBO 3AD LAD AAGDE AACO Statements ADEN DC A D D Given C Reasons Bisector 2 s 3 Reflexive Roperty SAS AE After completing the proof above a student in your class claims that AB BC Is the student s claim right or wrong Explain why 3 poi

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

If AB DE and AC DF which statement does NOT allow you to conclude that AABC ADEF A BC EF B LA LD C ZA and ZD are right angles D LB LE yriw nislaxs of beau 9d 60 me10ert w woladelgmsmit no bez B F menosdT asignA 9268 A C E 643

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

S 4 Consider a rectangular box with one of the vertics at the origin and point A 2 3 5 as shown Determine the angle between BC and BA Round to the nearest degree ZA B A 2 3 5 C

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

8 Using vectors explain how to determine the volume of the following parallelepiped Determine its volume B 6 3 5 A 4 0 0 x O C 2 3 5 D 6 5 3

1 Consider the vectors a 2i k b 4i j 3k and c i 4j 3k determine the following fully simplified b 3b 2c a a b c c 1 e exb 2 g Vector projection of bonto c 2 d x 1 f b c

11 The scalar projection of a onto b is 8 If the length of a is 11 then what is the angle to the nearest degree between a and b

9 Explain why it is not possible to determine a vector that is mutually perpendicular to vectors 2 1 and b 2 2

Complete the following proof en E is the midpoint of AB and CD

35 DEVELOPING PROOF Complete the proof of the Third Angles Theorem GIVEN LA LD LB LE PROVELC LF Statements 1 LA LD LB LE 2 m m m m 3 mLA mLB mLC 180 mLD mLE mLF 180 4 mLA m B m C mLD mLE mLF 5 m D m E m C mLD mLE mLF 6 m C m F 7 A B 1 2 3 Reasons 4 5 C D 6 7 Def of s E F

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

coordinates 10 8 6 4 2 R S S R 104 8 6 9 4 2 2 4 6 8 10 2 4 ection over the x axis T 6 U 8 X 10

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

Nate heard stories about the massive Sierra redwoods in California and looked forward to seeing one of these trees for himself On his first actual encounter with one of the trees Nate wants to know just how tall the tree is He places a mirror on the ground and experiments several times until he determines the correct distance from the base of the tree as well as the correct angle of incidence that allows him to see the top of the tree 1 9 m

Find the volume blank 1 and total surface area blank 2 of this solid shown below 3 cm 4 cm Blank 1 Blank 2 5 cm 7 cm A A

C 20 132 0 m B A 121 0 m

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

B side a a 55 A C 52 cm

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

Y side h 40 h Z 300 0 m H

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