Geometry Questions

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

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

In an isosceles triangle ABC with AB AC the bisector of angle C meets side AB at D if BC AC AD then A ZA B C T 3 3 8 C length of angle bisector CD 4 2 2 AB cos D length of angle bisector CD 4 2 2 AB cos RO ROO 8 TC 8 N REDMI 7 CAMERA

f 1 cose sine sine 1 cose 2csc0

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

1 Follow the steps below to help you prove or disprove that the point 1 15 lies on the circle that is centered at the origin and contains the poin 0 4 To earn full credit you must show your work Step 1 Plot a point at the origin and at 0 4 Use these to help you draw the circle centered at the origin that contains 0 4 Step 2 Determine the radius Step 3 Use the radius and the coordinates of the center to write the equation of the circle Step 4 Substitute the x and y coordinates of the point 1 15 in the equation of the circle to check whether they satisfy the equation

A hot air balloon is floating above a straight road To calculate their height above the ground the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon The angles of depression are found to be 16 and 19 How high in feet is the ballon Hint

Find the value of y K Fro 28 H

Find the circumcenter of the triangle 15 10 86

Find the value of x 84

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