2D Geometry Questions and Answers

Given the following parametric equation x t 4t 4 y t 2 for t 1 choose the graph that has the most accurate and complete curve and includes th correct orientation given the limits on t values Be careful here Look closely at the points plotted before making your choice Double check that the orientation is correct Double check endpoints arrows

MM wannn The sketch shows the graphs of the functions f and g The function f is defined by y acosk t b 4 2 For the function g determine a the value of m 4 3 y mcsc c x d b the period c the constant C d the constant d and then e write down the equation that defines g a Suppose we shift the graph of f vertically downwards by h units such that the maximum turning points vertices of the resulting graph lie one unit below the X avis What is 31 2

B 3X 20 2X 1 X 1 CHUPARANEN GRA STE

9 Find the area of the quadrilateral ABCD if AD BH HC 16 cm AB HD DC 10 cm B 10 16 A 2 points 16 H 10 D 16 10

6 The ratio of the measure of the complement of an angle to the measure of its supplement is 5 14 Find the measure of the angle 2 points

11 Given AB OD in circle O Prove mBD MAQ Proof 1 AB OD Statements 2 41 42 and m 1 m 2 3 m 2 mBD 4 m21 1 mAQ 5 mBD mAQ 1 Given 2 3 4 5 3 points A Q Reasons 0 B D

2 Given PQ LMN 4122 Prove AMQP ANOP Proof Statements 1 PQI MN and 21 22 2 ZMQP ZNQP 3 PQ PQ 2 points 4 AMOPANOP 1 Given 2 3 4 M P e Reasons N

3 Given m ADC 168 m BDC 2x 4 m ADB 3 m BDC Find x and m BDC D 2 points B

14 Given Im and t is a transversal If m 1 x x 4 7 and m28 x 2 x 1 Find x and m 1 2 points 1 2 3 4 5 6 7 8 24 m

13 Find the exact area of the sector Radius of the circle r 10 cm and m AOB 120 A 10 0 2 points 120 B

8 Given mAB 112 mDC 34 Find m1 and m 2 4 points B D E C 2

12 Given Rectangle ABCD is inscribed in the circle AD 8ft AB 6 ft Find the exact area of the region between the circle and the rectangle 4 points B 8ft 6ft D C

7 Given AABC with angles as shown AD 4 Find AB C 30 th A 4 D 2 points B

Please show your work No credit will be given for answers without supporting work 1 Determine whether the statement is true or false 1 point each a The consecutive angles of a parallelogram are supplementary b An inscribed angle can never be an obtuse angle c The bisector of the vertex angle of an isosceles triangle bisects the base d The complement of an angle is an obtuse angle

1 Triangle PQR is drawn with QR 4 75cm PR 7 25cm and ZPQR is O 19 1 or 160 9 O 49 7 O 19 1 49 7 or 130 3

Find the coefficient of the ab7 term in the expansion of a b In the expansion a b a Enter ONLY the coefficient a b7 b 3

he solid below is made from 1 foot cubes Find the total surface area of the solid Be sure to include the correct unit in your answer 1 foot 0 ft X ft ft

The proper angle for a ladder is about 75 from the ground Suppose you have a 20 foot ladder How far from the house should you place the base of the ladder 1

Solve the equations on the interval 0 2 2 sin x 1 0

Use the power reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1 17 sin x 4 17 sin x www

The units are in feet 5 Imagine you are tutoring your best friend in Geometry explain to them the process they should go through to determine the area of the shaded region B i Font Family AA VE

20 10 Use the Pythagorean Theorem to set up an equation to solve for x x 11 Solve forx Ox 5 13 Ox 5 5 Ox 14 Ox 25

4 Complete the triple 8 x 17 x

Question 1 Points 3 What three dimensional figure models the following object O Rectangular prism O Square pyramid O Sphere

Question 10 Points 2 The exterior of a spherical water tank is to be painted The radius of the tank is 4 feet How many square feet will need to be painted Use 3 14 4 square feet 96 square feet 200 96 square feet 20096 square feet

ces F 0 7 Find the total area surface area of a regular hexahedron if each edge has a length of 4 2 cm

In Exercises 10 to 12 the probability is the ratio number of favorable outcomes Use Example 2 of this section number of possible outcomes as a guide 10 Assume that a die of the most common shape a regular hexahedron is rolled What is the likelihood that a a 2 results b an even number results c the result is larger than 2

In Exercises 31 and 32 use the calculator value of T 31 For a sphere whose radius has length 3 m find the approximate a surface area b volume

15 Find the total area surface area of a regular octahedron if the area of each face is 5 5 in

An equilateral triangle is shown below Line w passes through a vertex and bisects a side Line u bisects each side it passes through Point P is the center of the triangle H P Which transformation s must map the triangle exactly onto itself Choose all that apply Reflection across line w Reflection across line u Counterclockwise rotation about P by 72 O Clockwise rotation about P by 240 None of the above X

polyr A polyhedron not regular has 10 vertices and 7 face How many edges does it have

1 The oblique circular cone has an altitude and a diameter of base that are each of length 6 cm The line segment joining the vertex to the center of the base is the axis of the cone What is the length of the axis 6 cm 6 cm

radius of the circular base find the dimensions of the can 12 Find the height of a storage tank in the shape of a right circular cylinder that has a circumference measuring 67 m and a volume measuring 817 m

In Exercises 15 to 20 use the fact that r h 1 in a right circular cone Theorem 9 3 6 16 Find the length of the slant height of a right circular cone with r 52 ft and h 39 ft

In Exercises 23 to 26 find the exact areas of the shaded region 23 8 in 8 in

3 In the semicircular region shaded DQ a Find the exact perimeter of the region b Find the exact area of the region C Q Exercises 3 4 D 6

5 In the circle the radius length is 10 in and the length of AB is 14 in What is the perimeter of the shaded sector B Exercises 5 6

4 Find the approximate circumference and area of a circl whose diameter has length 20 cm Use 3 14

In a particular type of regular polygon the length of the apo them is exactly one half the length of a side What type of regular polygon is it

5 In a regular polygon each interior angle measures 135 If each side of the regular polygon measures 4 2 cm find the perimeter of the polygon

15 Find the area of an equiangular triangle with apothem a 4 6 in and perimeter P 27 6V 3 in 16 Find the area of a sauore with anothom a ft and

In Exercises 17 to 30 use the formula A area of the regular polygon described ap to find the 20 Find the area of a regular octagon with an anthem of length

7 AABC is an obtuse triangle with obtuse angle A ADEF is an acute triangle How do the areas of AABC and ADEF compare A Exercises 7 8 8 B h 6 D 8 E

0 In a triangle whose area is 72 in the base has a length of 8 in Find the length of the corresponding altitude

5 B A 4 ft 7 ft 13 ft D Trapezoid ABCD with AB DC 6 X 3 5 2x

In Exercises 9 to 18 find the areas of the figures shown or described 9 A rectangle s length is 6 cm and its width is 9 cm

23 A triangular corner of a store has been roped off to be used as an area for displaying Christmas ornaments Find the area of the display section 24 ft

centimeters in I cubic meter 19 Given that 12 in 1 cubic foot 1 ft find the number of cubic inches in

The units are in yards 612 2 What is the measure of the radius of this circle T yd What is the area of this circle A Tyd 3 Explain the process you went through to determine the measure of the radius for the BiU U Font Family AA A PHN F

B X 18 8 P X Solve for x x 9 PQ is a Mid segment of A ABC A ABC A APQ 7 Since the Triangles are Similar we can use Proportions to solve for x 8 We can solve this proportion by CROSS MULTIPLYING 9