Geometry Questions

B C A is a right angle and C 30 13 Set up an equation to model this information use B for the m Use the button to input the equation Write your answer WITHOUT spaces 14 Solve the equation for B

Using the equation to determine the following for the next two questions 3 y 9 81 10 Find the Center of the circle 11 Find the Radius of the circle units

15 Name the property AB CD then AB EF CD EF O Reflexive Property O Symmetric Property O Transitive Property O Additive Property

8 Find the radius The units are in feet feet 16

12 What is the relationship between angle a and angle Oasb Oa b O a b O a b b

Using the figure below to determine the following for the next three questions 1 Name a Secant line O AF GH EB DC 2 Name a Central Angle

4 If AB is 30 feet find the diameter of the circle feet 5 Explain how you got your answer A What properties did you use B What formula did you use

23 Consider any triangle and one exterior angle at each vertex What is the sum of the measures of the three exterior angles of the triangle

1 3 18 Given Prove Statements 1 e m 2 1 2 3 42 43 e m 23 44 e n 4 5 L1 24 6 PROOF n l m 4 2 1 3 Reasons t 1 2 3 If two lines intersect the vertical Zs formed are 4 Given 5 Transitive Property of 6

j k 15 Given Find B 5 4 A 3 6 2 1 C m 1 122 3 m 5 41 5 m 2 m 3 and m 4

21 Given Prove DE bisects LCDA 23 41 ED AB E A 1 32 D B

3 In Exercises 7 to 16 name the lines if any that must be parallel under the given conditions Al p q 1 2 78 13 14 19 20 Exercises 7 16 7 21Z20 8 3 210 9 19 214 10 47 211 11 Ip and n I n 3 3 4 9 10 15 16 21 22 An 5 6 11 12 17 18 23 24

In Exercises 1 to 6 and m are cut by transversal v On the basis of the information given determine whether must be parallel to m 1 m1 107 and m25 107 2 m2 65 and m 7 65 3 m 1 106 and m 7 76 4 m 1 106 and m24 106 m 1 2 3 4 5 6 7 8

In Exercises 1 and 2 which sentences are statements If a entence is a statement classify it as true or false 1 a Where do you live b 4 7 5 c Washington was the first U S president

A way of describing points that lie on the same plane A way of describing a set of lines or curves that never meet or intersect A way of describing a line which crosses another line forming a right angle Choose Choose Choose

Instructions Your job is to add each of the four bases to the simulated spill to determine exactly how much of each is required to neutralize the acid Remember that neutralizing means to make the pH 7 This process of determining the amount of a chemical needed for a certain reaction is called a titration Chemical Magnesium Hydroxide Mg OH 2 Laboratory Acid Base Neutralizaton keachokd Reactions The Perfect Storm Spill Drill Sodium Hydroxide NaOH Sodium Carbonate Na CO Calcium Hydroxide Ca OH 1 Shovels required to neutralize acid Amount required to neutralize the acid 500 kg per shovel kg 500 kg cost per 1000kg 3085 Cost per 1000 kg kg 330 308 88 88 Total Cost I

For each of the following right triangles set up a trigonometric ratio involving ZA and then find the measure of ZA by using the appropriate inverse trigonometric ratio Round to the nearest whole degree b a c A B 18 6 10 A 7 B d B 14 CO A 28 A 12 B T 20 22

7 Parallelogram ABCD has coordinates of A 7 1 B 2 3 and C 0 3 What must be the coordinates of point D Explain how you found your answer y

Given that ABCD is a parallelogram with diagonals intersecting at M Segment PQ is drawn such that P lies on AB and Q lies on DC and it passes through M Prove that PM QM A P M B

1 In the diagram below ZDEF has been reflected in line t by reflecting points D E and F a As in class draw in segments DD EE and FF Mark the intersections of the segments with the line t b What is true about the points that you marked in part a Verify using an appropriate tool c What is true about the angles that the segments make with line t Mark these on your diagram D D E E tractor that the two angles are equal F

Given sin a 0 781 and sin 0 936 with both angles terminal rays in Quadrant l find the following Round your answer to 3 decimal places as needed tan a 8

6 A ladder leans against a building that is perpendicular to the ground such that it makes a 74 angle with the ground and its bottom lies 2 75 feet from the base of the building a Determine the height that the ladder reaches up the wall to the nearest tenth of a foot b How long is the ladder Round to the nearest foot 74 2 75 ft boooooo HH

If sin a 0 444 and sin 0 774 with both angles terminal rays in Quadrant l find the values of cos a 3 sin a 3 Your answers should be accurate to 4 decimal pla

5 An isosceles triangle has legs of length 12 and base angles that measure 28 What is the measure of its bas to the nearest tenth Be careful on this one

PROBLEM SOLVING 1 In each diagram shown below solve for the length of side CD using the information given Show the trig ratio you use and your algebra to find your final answer Round all answers to the nearest tenth b c a D 15 E E D 75 32 43 C d D 56 35 D 27 28 B B

4 In rectangle ABCD shown below CD 24 and m ABD 35 Determine the length of diagonal BD to the nearest tenth Show the work that leads to your answer A B 35

3 In AQRS ZR is a right angle m Q 57 and QS 35 Which of the following expressions correctly calculates the length of QR 1 2 35 sin 57 35 cos 57 3 35 cos 57 4 35 tan 57

Assume lies in quadrant 3 and the terminal side of 0 is perpendicular to the li y 19 x 6 Part 1 Determine sin e Part 2 Determine sec 8 sin 8 sec 8 X

cos u sin 2u cos 2u tan 2u 336 125 73 24 25 25 336 527 2 U X X

Given right triangle ABC shown below do the following a Measure the three side lengths to the nearest millimeter AB BC sin A b Based on your measurements in a state the value of each of the following in decimal form Round to the nearest thousandth cos A AC c Given the partial table of trigonometric values shown below which angle in the table is closest to the m A Verify using your protractor tan A Angle 37 38 39 40 41 A sine 0 6018 0 6157 0 6293 0 6428 0 6561 cosine 0 7986 0 7880 0 7772 0 7660 0 7547 B tangent 0 7536 0 7813 0 8098 0 8391 0 8693 0 0001

Students often struggle with the following statement All squares are rectangles but not all rectangles are squares Based on your knowledge of rectangles from this lesson and your knowledge of squares from middl school why is this statement true

4 Although it may seem obvious from the diagram of rectangle ABCD pictured ADMC is isosceles Explain why this must be true M

Given quadrilateral EFGH with vertices at E 4 8 F 8 4 G 5 5 and H 7 1 prove using coordinate geometry that EFGH is a rectangle Note that there are a few different methods that work y

10 Consider the definitions of the sine and cosine ratios Why can their values never be greater than 1 Use the triangle below as reference to help you answer C

A square has its length and width increased by two feet and four feet respectively so that it is now a rectangle The perimeter of the new rectangle is eight feet less than twice the original perimeter What was the original perimeter Show all work that leads to your answer Hint Let x square If you cannot do an algebraic approach at least attempt it by guess and check the side length of the original

4 Square ABCD has vertices at A 8 1 B 3 6 and D 3 10 What are the coordinates of point C TL

4 8 In the following diagram AEFG AMNP and cos E If MP 20 then find the length of MN to the 7 P nearest tenth Show the work that leads to your answer G S 20

4 Given that RSTU is a parallelogram and ST TU explain why RSTU must also be a rhombus R

C A rhombus has a perimeter of 80 inches Its longer diagonal is 32 inches Explain why the shorter diagonal must be 24 inches

In the following diagram of AQRS QR 8 and QS 17 Determine the value of sin Q Show how you arrived at your answer Q 17 8

3 In the diagram below of rhombus ABCD ADAC Which of the following is the measure of ZBDC A B 1 30 2 45 3 60 4 75 D E C

Construct a line AB such that it is parallel to RS shown below Use only a straightedge and compass Leave all construction marks Hint plot a third point not on the line and rotate about this point S

Given the rotation of AABC shown below determine the counter clockwise angle of rotation that occurred about point D Show all relevant lines and measurements you made to determine your answer A A C B C

E Using only a straightedge and a compass construct the image of AEFG after a rotation by 180 about point K shown Leave all construction marks Mark the image AE F G E K

5 Given the triangle below answer the following a Write trigonometric ratios based only on the information given for ZL and ZN ZL ratio ZN ratio b Solve both of these for the measures of ZL and ZN to the nearest tenth c What is the relationship between these two angles 10 5

I Given the right triangle shown below with m A 67 measure each side length to the nearest millimeter and then fill out the table For the ratios express your answers in decimal form to the nearest hundredth BC AB AC b cos cos 67 BC AC AB AC BC Making sure your calculator is in DEGREE MODE evaluate each of the following and verify that they either match or are close to the ratios you found in 1 a sin 67 c tan 67 AB A 67 C

3 Given right triangle DEF shown write down each of the following ratios Do not express as decimals a sin D b cos D c tan D d sin F f tan F e cos F 15 D 12 4 In any right triangle what must be true about the sum of the measures of the two acute angles Do you notice anything shout ho ging and cogine of the acute angles in 32 What do you notice

Joey wishes to contribute three items to a gift box He aims to pick from seven particular items Find the number of ways he can select the three items from these seven items Select one a 45 b 210 c 35 d 220

In trapezoid MNPQ shown below MN OP m M 108 m P 4x 15 and m Q 3x 21 Explain why m N must be 127 M N

7 Quadrilateral EFGH has vertices at E 1 8 F 6 1 G 4 4 and H 9 5 a Prove that EFGH is a parallelogram b Prove that EFGH is not a rhombus Many methods