2D Geometry Questions and Answers

Johnny is wanting to prove that parallelogram ABCD is a rectangle He shows that opposite sides are congruent and opposite sides are parallel Can he conclude ABCD is a rectangle Why or why not Explain your reasoning in complete sentences

Parallelogram ABCD is shown below D C B Which pair of triangles can be established to be congruent to prove that ZDAB ZBCD A DAB and A BCD A AED and A BEC A ADC and A BCD A DEC and A BEA

Given the quadrilateral is a parallelogram solve for x L K 10x 10 I Ox 20 Ox 4 Ox 7 x 10 N

What could be shown about the diagonals of parallelogram PQRS to complete the proof that diagonals of a parallelogram bisect each other P r t BI R s 0 S 0 0 r s t PR is a perpendicular bisector of SQ Angles formed by the intersection of PR and SQ each measure 90 PR and SQ have the same midpoint RR and So have the same length

What is the length of RS V R W X 3 x 5 S X

Listen What is the mZG F 20 G H

Given lines n and r are parallel 22 and 2 7 are P 1 2 3 4 5 7 6 8 n r

Once the construction below is complete creating a parallel line to PS through point Q which of the reasons listed contribute to proving the validity of the construction P P Q W T To T O When two lines are cut by a transversal and the vertical angles are congruent the lines are parallel Definition of segment bisector When two lines are cut by a transversal and the correspondina anales are Sign out

Given A ABC with points A 1 2 B 4 3 and C 0 0 dilated about a center at the origin by a scale factor of 3 an c

The figure shows the results of a construction of the bisector of ZP Order the following steps for this construction using the numbers 1 4 Ex the first step is 1 second step is 2 and so on V Using a straightedge draw the line through P and X Name the intersection of the two arcs X Draw an arc centered at P to create points Y and A Draw two intersecting arcs with the same radius one centered at Y and one centered at A on the interior of ZP

Find the length of an arc that subtends a central angle of 310 in a circle of radius 7 km arc length km Answer must be exact Use pi for and enter answer using a reduced fraction

One way to show that two triangles are similar is to show that two angles of one are congruent to two angles of the other an angle of one is congruent to an angle of the other a side of one is congruent to a side of the other two sides of one are proportional to two sides of the other

Write a similarity statement for the following triangles Be sure to match up the correct corresponding proportional sides M 6 N O

Solve for x Remember to match up corresponding parts by the similarity statement ADCBATSR C T 38 21 33 R 15x 11 Ox 11 x 21 x 17 x 8 B 38 98 S D

What is the reason for 4 Given DE BC Prove AD AB DB EC Statement 1 DE BC 2 mzA mZA 3 m AED m ACB 4 AACB AAED AD 5 AB AE EC 6 AD DB AB AF FC AG B Reason 1 2 3 4 5 6

Listen What is the reason for 4 Prove Corresponding Angles 7 5 3 8 1 6 2 m n Given 23 and 27 are corresponding angles Prove 43 27 Statements 1 23 and 27 are corresponding angles 2 3 26 27 4 3 27 Reasons 1 2 3 Vertical Angles Congruency Theorem 4

If statement 3 is ZPORZEOV what would be the reason Given VO RO and PR VE R E 1 2 3 4 Statements 5 APRO AEVO Given Given Reasons

Choose all quadrilaterals in which the property applies All angles are congruent Parallelogram Rectangle Rhombus Square Trapezoid Kite

If statement 2 is 21 24 what would be the reason Prove Alternate Exterior Angles 3 5 6 7 8 1 2 4 m t Given 41 and 48 are alternate exterior angles Prove 41 28 Statements 1 41 and 28 are alternate exterior angles 2 3 4 21 28 Reasons 1 2 3 4 Substitution Transitive Property of Equality

Use the graphs to evaluate the expressions below 6 5 4 3 2 1 1 1 f x 1 f g 3 g f 2 f f 1 g g 5 2 3 4 00 X 6 5 4 3 2 1 5 6 1 9 F 1 g x 1 2 3 4 5 X 6

Find the missing side length Show all work X 61 14

Listen What is the value of x 9 45 y X

Solve for x Show all work using the equation editor y 45 X 4

Solve the following for 0 in radians where 0 0 2 4 sin 0 9 sin 0 6 0 Round to the nearest hundredth Provide your answer below

Which Trigonometric Function is NOT equivalent to the other expressions Select one a cos 0 cot O b sec csc OC d tang sin 0 sin cos

end behavior of the Sorry that s incorrect Try again End Behavior 10 10 10 5 5 f x X 3 X 2 10

3 2 1 3 2 1 7 2 3 bo A 10 In the above graph estimate the slope of the tangent line at x 1

When graphing y 3cos 3x 4 the amplitude is the period is the phase shift is t

110 on is represented by the graph below 10 5 Select one O a y cos x 4 O b y 4sin x Oc y 4 sin x O d y cos x 4 5 0 5 10 5 10

Find the surface area of the cone to the nearest tenth O 213 5 cm Not drawn to scale 2 O 203 cm O 747 7 cm 7 cm 2 O 1341 5 cm 27 cm

Solve the following equations Round your answers to the nearest hundredth as needed TIP Do not round until you get to your final answer 4 856 11 31 7 47 b 7 79 9 83w 3 61 7 77 W 6 39 5 61n4 37n n R 6 05R 3 65 R

Plots of land between two roads are laid out according to the boundaries shown The boundaries between the two roads are parallel What is the length of Plot 3 along Cheshire Road 40 yards PLOT 1 C 48 yards O 74 yards 2 PLOT 2 O 53 yards Cheshire Road yards Shelby Road 4 PLOT 3 64 yards PLOT 4

Linear Equations When a new charter school opened in 1993 there were 440 students enrolled Write a formula for the equation N representing the number of students attending this charter school t years after 1993 assuming that the student population Increased by 36 students per year Decreased by 24 students per year Increased by 20 students every 2 years Decreased by 40 students every 4 years Remained constant did not change Increased by 5 students every semester twice each year N N N N N N II

2 In the accompanying diagram tangent PA and secant PBC are drawn to circle O If mADC is twice mAB and m P is 50 what is mAB C 0 A 50 P

What are the minor arcs of 00 H L OJK and LH J HJ and KL K HJ HK JK JL KL and LH HJ JK KL and LH

Find the area of the rhombus 9 m 6561 m O 162 m O 13 5 m 40 5 m 9 m 9 m 9 m

Identify a semicircle that contains C A O ABC CB 0 B

C Directions Complete the two column proof 10 15 Given A LMN where IM IN MN Prove MN IN IM MN LM IN ZM IN MN 1 2 3 Statements 1 2 3 N Reasons

What is the solution of each proportion D 5 A 120 10 10 C bo B 5 Not drawn to scale N 3 12 M 120 1 2 O ABCD KIMN 10 1 2 1 2 The polygons are not similar O ABCD NKLM 5 3 12 O ABCD KIMN 5 1 2 K 3 12 L

What similarity statement can you write relating the three triangles in the diagram T U V ATWV AVUW AUWT O AWUT AVUW AWVT O AUVW AUWT AWVT O AUVW AWUT AWVT

Segment BD bisects segment AC Solve for x Round to the nearest tenth if necessary Image not necessarily to scale A 20 Answer p 8 B D 17 X

Which trigonometric statement is NOT an identity Select one a cse 0 1 cot 0 b 1 cos sin 0 c 1 sin 0 cos 0 Od 1 tan 0 sec 0

Solve each equation to the nearest tenth Use the given restriction tan 1 4 for 180 270

7 10 points Given ui 5j and v 3i 4j find i the dot product u ii 2u 3v

rom what you learned about radians which circle best represents how radians are meas elect one a O b OC 66 42 44 41 41 a 44 SA a 41 44

Use an addition or subtraction formula to find the ex sin 67T 44 COS 3T 11 COS 67T 44 sin 3 T 11

ividing sin 0 cos20 1 by yields 1 cot csc

Find all the values of arcsin 3 Select one or more 0 0 a 3 b 5 C KM 0 e f d 7 g 3 5n 6 6 2x 3 4 3 11x 6

The angle 810 rotate clockwise counter clockwise full time s around the origin and is radians

Simplify the following Hint Use the unit circle sin 5m 3 Select one O a 1 2 Ob undefined OC 3 2 d 3 2