2D Geometry Questions and Answers

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

he given point on the unit circle find the six circular function values for s 8 X 17 the value of x or y as appropriate Then assumin X 0 Type an integer or a simplified fraction www

Graph the rational function Answer parts 1 through 7 below X 1 Select the symmetry of the function O The function is symmetric about the y axis O The function is symmetric about the origin O The function has no symmetry about the y axis or the origin 2 Find the y intercept Select the correct choice below and fill in any answer boxes within your choice OA The y intercept is Type an integer or a simplified fraction OB There is no y intercept 3 Find any x intercepts Select the correct choice below and fill in any answer boxes within your choice OA The x intercept s is are Type an integer or a simplified fraction Use a comma to separate answers as needed OB There are no x intercepts 4 What are the x coordinates of the vertical asymptote s Select the correct choice below and fill in any answer boxes within your choic OA x Use a comma to separate answers as needed COL OB There are no vertical asymptotes 5 What is the y coordinate of the horizontal asymptote Select the correct choice below and fill in any answer boxes within your choice OA y OB There is no horizontal asymptote 6 Type the y coordinate for each of the following points 2 2 4

estion 8 estion 9 estion 10 T corresponds to x Then findcos x andsin and state which functions are undefined for The point on the unit circle is Type an ordered pair Type an integer or a simplified fraction 1 0 2 0 1 0 0 1

4 The point on the unit circle is Type an ordered pair Type an integer or a simplified fraction 1 0 2 0 1

aces Dx where b 0 Determine the equation of the

50 Find the length of the pulley belt shown in Fig 2 87 if the belt crosses at right angles The radius of each pulley wheel is 5 50 cm C Fig 2 87

Let sec A 2 with A in QIII and sec B 5 with B in QII Answer exactly Find sec A B

coterminal with the given angle The correct expression is 315 Type an equation using n as

ind the angle of least positive measure in degrees not equal to the given with A 65 Simplif

roblem 3 A rectangular plot of land is to be enclosed by a fence Furthermore an additional section of fence is set parallel to one side cutting the plot into two smaller rectangles If 288 meters of fence are available what is the greatest area of land that can be fenced in this manner

oblem 2 Suppose that a right triangle has legs of lengths 7 cm and 5 cm Note that the legs of a right triangle are the two sides that are not the hypotenuse A rectangle is inscribed in this right triangle so that two sides of the rectangle lie along the legs Find the largest possible area of such a rectangle

36 Given KN bisects JM JK MN M K Prove AJKLAMNL N

32 Given R is the midpoint of PT 4P T and PRQ TRS Q M R PA Prove APQREATSR S AT 800

35 Given PQRS is a parallelogram P Q R Prove ARPS AQSP S OR T X IN

23 Given 4P ZS ZQ LT and QR TU AT RS Prove APQR ASTU P

A large warehouse has dimensions as shown The owner has it subdivided so that he can lease storage space to two businesses The area of the smaller space is 60x ft How could you express the area of the larger space in terms of x a 100 60 ft 100 x ft b 60 2 ft 60 100 C 3x d 60 100 x ft a 60 feet 100 feet

Select the correct equation of the following graph 10 10 10 10

Write a rule to describe each transformation 19 X X W W Y

1 By using the midpoint formula show that the axis of symmetry of the parabola b 2a y ax bx c is x uloz 1091 vnom woH 21500 d

Graph the equations b y 4 3 x 2 7

What mass of reactants are used during the reaction Hydrogen Bromine Hydrogen Bromide 16 25 g g Give your answer to the correct number of significant figures g Hydrogen Bromide

Triangle sum theorem The sum of the interior angle measures of a triangle is 180 A D 1 Proof B 1 DE 2 Given AABC with DE AC Prove ml m 2 m 3 180 2 21 DBA 3 C F 3 m1 m DB 1 Civer Oiver

Refer to the given diagram with FB DE Which figure has the greatest measure Om ACE O Arc BD O m FBE D 78 F 50 E

The graph of f x 5 0 15 is given below click on graph to enlarge

b C 3 9 D 5 4 Find the midpoins of set of orderd pairs

1 Name the transformation that maps the lighter turtle preimage to the darker turtle image a b c 2 Tell whether the transformation appears to be an isometry Explain your answer t

Steps for graphing a rational function to graph the function P x 1 The graph has y intercept and no x intercept 6 Simplify your answer Type an integer or a fraction OD The graph has neither x intercepts nor y intercepts 6 36 X Determine the behavior of the graph of P at any x intercepts Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The graph will cross the x axis at x and touch but not cross the x axis at x Type integers or simplified fractions Use a comma to separate answers as needed Type each answer only once OB The graph will touch but not cross the x axis at x Type an integer or a simplified fraction Use a comma to separate answers as needed Type each answer only once OC The graph will cross the x axis at x Type an integer or a simplified fraction Use a comma to separate answers as needed Type each answer only once OD There is no x intercept

7 Use your compass to construct two circles with the same radius intersecting at two points Label the centers P and Q Label the points of intersection of the two circles A and B Construct quadrilateral PAQB What type of quadrilateral is it

5 a Draw the vectors a 3 2 b 2 1 and C 7 1 b Show by means of a sketch that there are scalars s and t such that c sa tb c Use the sketch to estimate the values of s and t d Find the exact values of s and t

13 16 Find a b 2a 3b a and a b 13 a 5 12 b 3 6

Would you use SSS SAS ASA or AAS to prove the triangles congruent If there is not enough information write There is not enough information Explain your answer E P F R

A chord AB of a circle centre O and radius 21 cm is 36 cm long Express the angle AOB in radians Use your result in a to calculate correct to three significant figures i the length of the arc AB the area of the sector AOB the area of the minor segment cut off by the chord AB Take 3 142 ii iii

Question 12 of 14 12 Assume each outcome in the sample space S provided below is equally likely Find P AB S 0 1 2 3 4 5 6 A 0 1 2 5 B 1 2 4 Round your answer to the nearest hundredths Answer Previous Answer 0 29

The medians of AABC are AE BF and CD They meet at a single point In other words G is the centroid of AABC Suppose BF 27 AG 14 and CG 20 Find the following lengths Note that the figure is not drawn to scale A D F G B E C GD 0 GF AE

36 reflection across the x axis v 5 1 W 5 3 X 1 3 AY X

2x 4 A C B 9 11 BC A A Sy 1 B y 2 C

An equation is given Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTI 3 tan 30 1 0 a Find all solutions of the equation Tk TUTU 3 18 8 8 X b Find the solutions in the interval 0 2 T 7T 4 6 X

An equation is given Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION 2 cos 38 1 a Find all solutions of the equation 8 b Find the solutions in the interval 0 2m 8

Given AC L BD and BD bisects AC Prove AABD ACBD Step 1 2 try Statement AC L BD BD bisects AC BD BD Type of Statement Reason Given Reflexive Property A B D C

Given E is the midpoint of BD and AC L BD Prove ABAE ADAE Step 1 try Statement E is the midpoint of BD AC L BD Type of Statement Reason Given A B E D

Given AD AE and AB AC Prove AABE AACD Step 1 try Statement AD AE AB AC Type of Statement Reason Given A D F B

Given D is the midpoint of AC ZAED ZCFD and LEDA LFDC Prove AAED ACFD Step 1 try Statement D is the midpoint of AC LAED LCFD LEDA LFDC Type of Statement Reason Given E B F

Complete the proof 1 Given Line AB intersects line DC at point B LAEB and DEC are straight angles Prove LAEC DEB 10 Statements E Reasons 1 1 2 ZAEC is supplementary to CEB 2 3 ZDEB is supplementary to CEB 3 Def of Supplementary Zs 4 4 Supplements Theorem a ZAEB and DEC are straight angles b Substitution c Angle Addition Postulate d Given e Addition Property of Equality f Linear Pair Theorem g ZAEC is congruent to ZDEB B