Geometry Questions

The two triangles below are similar Also mLH 20 and mI 100 as shown below Find mLX mLY and mLZ Assume the triangles are accurately drawn G I 100 m2x 0 m 2 Y 20 H X Z

Find an equation for the graph Type the equation of the given graph in the form y Asin Bx or y A cos Bx D otion Ico intogors or fractions for any numbers in the equation Simplify your answer 3 TU 2 JTC 5 3 14 IT

Suppose that AB AC AD AE and AF are coplanar F A B D E

Plot the complex number Then write the complex number in polar form Express the argument in degrees 9 9i Plot the complex number on the complex plane to the right AImaginary Real

27 Using the number line provided name the point that a is the midpoint of AE b is the endpoint of a segment of length 4 if the other endpoint is point G has a distance from B equal to 3 AC A E F 3 B 2 C 1 D 0 1 2 G 3 H 4

What relationship if any exists between two angles a with equal measures b that have the same vertex and a common side between them

31 Given Construct AB as shown in the figure PQ on line n so that PQ 3 AB A B

20 Suppose that point C lies in plane X and point D lies in plane X What can you conclude regarding CD

9 Name three points that appear to be a collinear b noncollinear 0 How many lines can be drawn through I a point A b points A and B c points A B and C d points A B and D A C Exercis

17 Given Find AM AB x and AB 2x 1 MB 3x 2 and 6x 4

4 Classify as true or false a AB BC AD CD AB CD AC b AD c AD A M B C D d AB BC CD AD e AB BC I

16 Given Find M is the midpoint of AB AM 2 x 1 and MB 3 x 2 x and AB

41 Find m ABC if m 1 42 and m 2 29 42 Find m 1 if m ABC 68 and m 1 m 2 43 Find x if m 2 x m 1 2x 3 and m ABC 72 A 1 B 2 D C Exercises 41 44

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

The polar coordinates of a point are given Find the rectangular coordinates of this point 3 3 2 What are the rectangular coordinates of this point Type an ordered pair Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

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

The radius of a wheel rolling on the ground is 80 centimeters If the wheel rotates through an angle of 45 how many centimeters does it move Express your answer in terms of and then round to two decimal places A The distance that the wheel moves is centimeters Type an exact answer using as needed Use integers or fractions for any numbers in the expression

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 55 and 56 P is a true statement while Q and R are false statements Classify each of the following statements as true or false 55 a P and Q or R b P or Q and R

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

For adults in the town of Bridgeport systolic blood pressure is normally distributed with a mean of 132 mmHg and a standard deviation of 10 mmHg What percentage of adults in the town have a systolic blood pressure less than 112 mmHg Use the 68 95 99 7 rule OO A 97 5 B 5 C 95 D 2 5

Which type of path straight curved circular or scattered is determined by a a roller coaster b a pencil c d darts thrown at a dartboard a carousel

17 Use the angle symbol 2 and three letters to name the angle formed by the two rays CD and CE rays not shown

2 Is the set named empty finite or infinite a L points on a line b B baseballs used in a major league game c N negative numbers that are larger than 5

9 What relationship subset intersect disjoint or equivalent can be used to characterize the two sets shown in the Venn Diagram A a B B A 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

7 Let A B and C lie on a straight line as shown near Exercise 8 Classify these claims as true or false a B lies between A and C b AB is a ray with endpoint B

At one college GPA s are normally distributed with a mean of 2 6 and a standard deviation of 0 5 What percentage o students at the college have a GPA between 2 1 and 3 1 Use the 68 95 99 7 rule A 99 7 B 84 C 95 D 68

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

11 For the sets given in Exercise 9 is there a distributive rela tionship for union with respect to intersection That is does AU BNC AUB n AUC

Reduce the spanning set to a basis for R S 2 2 1 3 2 1 2 3 0 0 2 1

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

The area of the triangle defined by the hyperbola s two focal points and the circle s NORTH point is NOTE b equals two Round your answer to the nearest whole number

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

Use the dot product to find the magnitude of u u 121 22j u 26