2D Geometry Questions and Answers

25 The sides of the pair of angles are parallel Are 21 and 22 congruent 2

37 Find x if AB x BC x 3 and AC 21

39 LABC is a straight angle Using your protractor you can show that m 1 m 2 180 Find m 1 if m2 56 A 1 2 B Exercises 39 40 40 Find m 1 if m 1 D C 2x and m 2 X UNT Son Exarcica 39

34 An angle is bisected if its two parts have the same measure Use three letters to name the angle that is bisected A B 10 10 15 C D F

21 Consider the square at the right RSTV It has four right angles and four sides of the same length How are sides RS and ST related How are sides RS and VT related V 22 Square RSTV has diagonals RT and SV not shown If the diagonals are drawn how will their lengths compare Exercises 21 Do the diagonals of a square appear to be perpendicula R

Polar coordinates of a point are given Find the rectangular coordinates of the point 7 90 The rectangular coordinates of the point are Type an ordered pair Simplify your answer including any radicals Use integers or fractions for any numbers in the expres

5 Suppose AB and CD have the same length Which state ments are expressed correctly a AB CD c AB CD b AB d AB CD CD

11 Which symbols correctly name the angle shown LABC LACB LCBA B

7 Name all the angles in the figure C

In Exercises 33 to 36 use intuition to state a conclusion 133 You are told that the opposite angles formed when two lines cross are vertical angles In the figure angles 1 and 2 are vertical angles Conclusion A 1 M 2 B Exercises 33 34 34 In the figure point M is called the midpoint of line segment AB Conclusion

14 If where b 0 and d 0 then a d b c

of each statement 11 If you go to the game then you will have a great time 12 If two chords of a circle have equal lengths then the arcs of the chords are congruent 13 If the diagonals of a parallelogram are perpendicular then the parallelogram is a rhombus 14 If 2 where b 0 and d 0 then a d b c 15 Corresponding angles are congruent if two parallel lines are cut by a transversal 16 Vertical angles are congruent when two lines intersect

In Exercises 19 to 24 classify each statement as true or false 19 If a number is divisible by 6 then it is divisible by 3

In Exercises 5 to 10 classify each statement as simple conditional a conjunction or a disjunction 5 If Alice plays the volleyball team will win I 6 Alice played and the team won 7 The first place trophy is beautiful 8 An integer is odd or it is even 9 Matthew is playing shortstop 10 You will be in trouble if you don t change your ways

For Exercises 13 to 16 consider the figure with the circle and lines AB CE and GF Classify the following claims as true or false 13 The circle and AB intersect in two points 14 CD nGF E 15 Two lines must intersect in one C D G E A F H B

21 If A 1 2 3 4 and B 2 4 6 8 find a N A b N B c N ANB d N AUB

9 Given A Find 1 2 3 4 B 2 4 6 8 and C a ANB b BUC c ANB N BUC 1 3 5 7 9

AB BC and BC CD AB 3x AB CD x 1 3 x 4 Statement 3x 1 2x 3 AB 11 BC 11 1 and CD 2x 3 AB 3 4 1

A Statement AB DE AC B D E Reason Substitution Property of Equality Simplify Division Property of Equality Given Multiplication Property of Equality Definition of Midpoint Definition of Congruent Segments Addition Property of Equality AB BC AC Subtraction Property of Equality Segment Addition Postulate Reflexive Property BC DE Transitive Property Distributive Property

E Part 1 of 2 18 BC 2 36 73 76 cm AC 2 40 B 56 16 cm a Find the lengths of BC AC DB DC ED EC cm DB A cm DC and E cm ED cm EC cm anc

The terminal side of angle 0 intersects the unit circle in the first quadrant at x 23 What are the exact values of sin 0 and cos 0 Provide your answer below

Answer Select the correct graph from options a to d Enter the intercepts as ordered pairs Separate multiple answers with commas Enable Zoom Pan 101 V 3 10 x intercepts 10 Enable Zoom Pan 701 V 35 35 f x x 3x 4 70 b x 10 10 Enable Zoom Pan 101 c V y intercept x 10 10 5 Enable Zoom Pan 101 y 5 10 Keybo d

points Graph the rational function f x Make sure you include all asymptotes on the graph a Find all x and y intercepts Write the answer in coordinate form x intercept s b Find all vertical asymptote s c Find all horizontal asymptote s Answer X y Answer x 3 x 5 by going through the following steps x 1 x 4 y intercept y 3 points d Plot at least two points on each side of the vertical asymptote s Graph the function Use dotted lines for all asymptotes 6 points 2 points 1 point

C E B elect one Check a BD RT b ZAEB ZQUR C CD ST Od ZCED ZSUT N D K G is the diameter of OM Which conclusion cannot be drawn from the diagram M L H Select one 8 R G a GH GL Oh IGGH S

If g x 4x2 16 were shifted 9 units to the right and 1 down what would the new equation be OA h x 4 x 17 9 OB h x 4 x 7 16 OC h x 4 x 9 17 D h x 4 x 9 17

In the diagram at the right the endpoints of the chord are the points where the line x 4 intersects the circle x y 49 What is the length of the chord The length of the chord is approximately Round to the nearest tenth as needed

Answer Check Determine whether a tangent line is shown in each diagram 9 4 5 3 10 6 5 6 12 10 3 3 6 Choose Choose Choose

Answer Check 70 The circle below represents Earth The radius of the Earth is about 6400 km Find the distance d that a person can see on a clear day from height h above Earth Round your answer to the nearest whole kilometer 20 km r 4 r

In OO mAB 60 and CA BD What is mCD mCD B

Find the value of x 8 4 1 0 X Do not round until the final answer Then round to the nearest tenth as needed

OA and OB are congruent CD is a chord of both circles If a radius is 13 ft and CD 10 ft how long is AB The length of AB is ft A B

Answer Check 40 0 Assume that lines that appear to be tangent are tangent O is the center of the circle What is the value of x that appear to be tangent are tangent O is the center of the circle What is the value of x 51

What is the most precise classification of the quadrilateral formed by connecting in order the midpoints of the figure below 4 SO 1Q Select one 3 R A rhombus X OB rectangle OC parallelogram OD square X

4 x degrees 5 Explain the process you went through to find the measure BiUFont Family AAT

Find what x equals and the measures of angles a b and c 15 To find we need to compare the two angles that have x in them 3x 7 and 5 These two angles are 16 Set up an equation to solve for x Use button to input the equation Input your answer WITHOUT spaces

21 Name all angles which are congruent c d O a and d b and c e and h g and f a and e b and g c and f d and h O a and c b and d e and f g and h a and b c and d e and g f and h

C 23 degrees side a 14 side b 12 find angle A angle B and side c

Find BC 25 B 3x 4 D 4x 5 C OBC 25 BC 62 BC 9 25 OBC 31

The endpoints of a diameter of a circle are 7 2 and 1 10

Complete the flowchart proof Then write a two column proof Given AD BC ADLAB ADLBC Prove AC BD A D Dfn of Perpendicular Lines Given ZA and B are right angles Given B C AB BA 100 ZA ZB AD BC Given SAS AC BD

determine the center foci and vertices of the ellipse and sketch the graph 23 x 4x 16y 32y 4 0

11 Find the anglex and lengths y and zin the following rhomb x y 2 6 degrees

70 9 Find x X 10 Find y 110 degrees degrees

4 What would be the best way to label this polygon Parallelogram 5 Find x degrees 6 Explain how you got your answer A What properties did you use D

11 Given m DAC 7 x 4 m B 2 2x 5 and m C 2 3x 1 Find x 2 points DA C

10 Lines XY and UV intersect at M m 1 7x 21 m 3 3x 7 Find x and mZ3 2 points 2 M

State the hypothesis and the conclusion of the statement 2 points If the diagonals of a parallelogram are congruent then the parallelogram is a rectangle Hypothesis Conclusion

7 Given 1m and t is a transversal If m 1 x x 4 7 and m 8 x 2 x 1 Find x and m 1 2 points 1 2 3 4 5 6 8 t m 1

8 Find the number of sides that a polygon has if the sum of the measures of its interior angles is 2340 2 points

6 Suppose line segments AB and CD have the same length Which statements are expressed correctly a AB CD b AB CD c AB CD d AB CD 2 points