2D Geometry Questions and Answers

24 A circle with center 1 2 passes through the point 2 2 Which is true a A radius of 5 c x 1 y 2 10 b The diameter is 10 d none of the above

What is being constructed in the sketch X OA angle bisector B circumcenter OC median OD perpendicular bisector

19 Given MP is a perpendicular bisector which of the following statements are true a AM MB b mz MPB 90 c m MB 8 d All the above A M X

22 What is the center of the circle given the following x 5 y 1 25 a 5 1 b 5 1 c 5 1 d 5 1

14 Given that B is the midpoint of line segment AC which of the following is NOT true a The distance from A to C is 5 units b Point C has the coordinates of 7 3 c The distance from A to C is 52 d The distance from A to B is equal to the distance from B to C B 5 0 4 3 1

18 Given the figure to the right if m OML 82 and the m LMN 158 then find m OMN L M

13 Find the value of x a 4 b 8 8 c 27 2 d 22 5x 13 12

25 All cell phone towers are experiencing technical difficulties except for the cell phone tower located at 0 0 which sends a signal with a radius of 8 Ryan Who can still communicate with his her cell phone a Makayla and Jasmine b Jamal and Mya c Amber and Mya d Amber and Ryan Amber Subpary HERZEZER preaf R patry Queen Mys Makayla Burger King Pobaves

12 Given the diagram to the right determine the values for x y z a x 76 y 76 z 76 c x 76 y 104 z 104 b x 76 y 104 z 76 d x 76 y 76 z 104 76 Z

9 Find the m 1 and mz2 a 21 67 m 2 67 b 21 113 m 2 67 c 21 113 m 2 113 d 21 67 m 2 113 67 2

6 A and B are complementary If mA 3x 1 and m B 2x 11 which of the following equations would you use to solve for x a 3x 1 2x 11 c 3x 1 2x 11 180 b 3x 1 2x 11 90 d 3x 1 2x 11

3 A bag contains letter tiles that spell mathematician Find the theoretical probability of drawing one tile at random and getting either the letter a or the letter m b 3 13 a 2 13 c 5 13 d 8 13

5 In the given figure m ABC 134 and BD bisects LABC Find the mLABD a 33 5 b 67 c 134 d 180

List the sides of the triangles from shortest to longest R 35 T 1 Shortest 2 75 3 A overline RT overline TA overline AR

List the sides of the triangles from shortest to longest B A Shortest 1 41 2 47 C Moverline BCN Moverline AC

Given BCDE and if AD x DB 2 AE 5 and EC x 3 find AD B A D C

Approximate the area under the curve graphed below from z 1 to 2 5 using a Left Endpoint approximation with 4 subdivisions 4 5 6 7 8

Segment JK has endpoints J 2 4 and K 6 2 You dilate the segment using a dilation centered at the origin with a scale factor of and then reflect the image over the x axis Where is the final image of K M

O 5 2 and 2a 2x what is the value of x N

12 What is a series of rigid motions that maps AABC onto ADEF C B A E 7 LL F X

PROVING A THEOREM Use the diagram to prove the Triangle Midsegment Theorem for midsegment DF where F is the midpoint of OC B 2q 2r D E A 0 0 0 C 2p 0 x The midpoint of OC is and BC F P 0 F p 0 F p 0 DF Because DF BC F 0 p Because the slopes of DF and BC are both equal to P 9 BC DF r P 9 r p q 1 1 20 p 2pq q p

Write the rule to describe the transformation U O Dilation of 0 25 O Dilation of 0 2 O Dilation of 2 5 O Dilation of 1 5 1 O None of the other answers are correct

Find the coordiantes of the vertices for the figure after the given transformation Dilation of 0 25 I 2 1 J 2 2 K 2 1 O I 0 5 0 25 J 0 5 0 5 K 0 5 0 25 O I 4 2 J 4 4 K 4 2 O I 5 2 5 J 5 5 K 5 2 5 O I 3 1 5 J 3 3 K 3 1 5 O None of the other answers are correct

Write a 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 Dilation of 0 5 Dilation of 335 2 O Dilation of 3 O Dilation of 1 25

and the given scale factor to find the coordinates of the vertices of the image of the polygon k 1 2 J K L M S M YA K L AX

Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon k 2 8 7 6 5 4 3 2 1 P Q 0 1 2 3 4 5 6 7 8 2345678 Q R D P

The midpoint of CD is M 3 3 One endpoint is C 0 2 Find the coordinates of the other endpoint D D M 3 3 c 0 2 D 00

Write the rule to describe the transformation C 2 1 D 2 2 E 1 2 C 4 2 D 4 4 E 2 4 O Dilation of 0 5 O Dilation of 2 25 O Dilation of 2 O Dilation of 2 5

Write the rule to describe the transformation C 4 5 D 3 1 E 5 3 C 2 2 5 D 1 5 0 5 E 2 5 1 5 Dilation of 0 5 Dilation of 0 25 Dilation of 3 Dilation of 1 25 Nong of the other answers are correct

Determine the scale factor Pre Image 5 3 2 3 2 1 5 1 10 6 4 6 4 2 10 Image 2

Date Name Fill in each blank with the correct angle line segment or angle measure using the proper notation AABC AJKL AEFG AWXY 65 1 65 B L 175x9 IN 29 5 cmX 1 ZA 2 ZB 3 ZC 4 AB 5 BC 6 CA 7 M C 8 MJ 9 MZK 10 mL F G 11 ZW W 25 90 12 ZX 13 ZY 14 WX 201 15 XY 16 TW 17 m Y 18 MZE 19 m F 20 m G

2 identify the graph the system of quadratic inequalities y z 2r 3 VS z 2 Big Ideas Math

7 What postulate proves the two triangles are congruent a AABC AFDE by ASA b AABC AFDE by HL c AABC AFDE by AAS d AABC ADFE by ASA B C E D

11 In parallelogram FRED shown ED is extended to A and AF is drawn such that AF DF If m R 110 what is mLAFD a 70 b 40 C 140 d 110 A F D R

A line perpendicular to Line AC would have a slope of 5 st 3 2 C A B b a C

3 m 12 m 4 5 marks 2 An architect is designing an asymmetrical log house similar in design to the following image D CI 5 The architect wants the house to be 15 m wide and plans to use 12 m logs for each roof line The height of the wall on the left is 3 m The following diagram can be used to model this house 12 m I II 6 1 15 m B Determine the angle 8 at the peak of the roof Make sure that your answer is rounded to the nearest 7

Find an objective function that has a maximum or minimum value at each indicated vertex 25 minimum at A Ay N A OD 27 maximum at B y B A O D B C X X 26 maximum at C AYA O D 0 28 minimum at D A A B D B X C X

1 2 3 4 5 6 7 U Statement VW E UY LVXW E LUXY XY L UY WX L VW ZY ZW AUXY AVXW VX UX X Y W Reason Given Given Given Given AAS ASA CPCTC

1 2 3 T 4 the proof that ZVTW ZTVU U Statement TU VW UV TW W TV TV ATUV AVWT 5 LVTW LTVU V Reason Given Given SSS AAS ASA CPCTC Definition of congruence SAS

AVXZ is equilateral and ZY ZW Complete the proof that XY WX Z 1 2 3 4 5 6 Y X ZY ZW Statement AVXZ is equilateral W LYXZ ZVXW XZ VX AXYZ AXWV XY WX V Reason Given Given Vertical Angle Theorem Additive Property of Angle Measure Additive Property of Length All right angles are congruent Angles forming a linear pair sum to 180 Definition of angle bisector Definition of equilateral triangle

What single transformation was applied to quadrilateral A to get quadrilateral B B Choose 1 answer 00 A Translation Rotation

4 Priya is teaching her younger cousin to ride a bike She wants to stay on roads that are not too steep and easy enough for a new bike rider She has decided the roads must have an angle less than or equal to 7 degrees A 7 degree angle in a right triangle has a 3 25 ratio for the legs List the legs of 2 right triangles that would be safe for a new bike rider

1 point Determine if triangle FGH and triangle IJK are or are not similar and if they are state how you know Note that figures are NOT necessarily drawn to scale H A 53 F G K 53 81 Similar SSS three sides proportional Similar SSS three sides congruent Similar SAS two proportional sides and included angle congruent Similar AA two angles congruent Not Similar the sides given are not proportional Not Similar there is only one pair of congruent angles

Consider the function f x 2x 3x 36x 54 a Find the first derivative f x b List any critical values c Identify intervals of increase d Identify intervals of decrease e Find the second derivaitve f x f Use parts b through e to identify maximums as points g Use parts b through e to identify minimumns as points h Use the second derivative to identify intervals where f z is concave up i Use the second derivative to identify intervals where f x is concave down j Use the second derivative to find any inflection points k Upload a sketch of the function based on the information above and the intercepts Choose File No file chosen

Consider a system of two nonlinear first order ODEs where r and y are functions of the independent variable t 2tanh r 2r cos y 1 3cosh z 3e y sin x a Write down in matrix form of the type X AX with X x y the system obtained by linearisation of the above equations around the point z y 0 Specify the elements of the matrix A b Find the eigenvalues and eigenvectors of the matrix A obtained in a Write down the general solution of the linear system e What type of fixed point is the equilibrium solution r y 0 Sketch the phase portrait of the linear system d Find the solution of the linear system corresponding to the initial conditions z 0 1 y 0 0 Determine the values lim r t and lim y t

following crosstabulation regarding their educational level and their monthly salary 1000 2999 ILS 55 15 The variable educational level has the Tawjihi Community College University Total Select one a ordinal scale of measurement O b interval scale of measurement O c ratio scale of measurement 3000 4999 ILS 35 95 20 150 5000 7999 ILS 10 25 50 Tot 10 14 60 30

Find the value of x for which m n m 3x 32 2x 27

Determine the 4th coordinate of parallelogram JKLM 6 4 2 6 4 2 2 4 6 2 4 M 6

If the lengths of the sides of a triangle are a b and c and the height of the triangle is longer than side c which describes the triangle a C h b

A dilation has center 0 0 Find the image of the point L 2 0 for the scale factor 7 L Type an ordered pair Simplify your answer www