Geometry Questions

Your family has decided to put a rectangular patio in your backyard similar to the shape of your backyard Your backyard has a length of 40 feet and a width of 32 feet The length of your new patio is 14 feet Find the perimeter of your new patio The perimeter of the patio is feet

rapezoid RSTU is a cross section of a lampshade The diagonals of RSTU are congruent and the measure of ZS is 112 What is the measure of U 112 R S ZU U

6C 13 Prove that quadrilateral ABCD is a rectangle B 4 A a qu 0 1 D M

Decide whether quadrilateral ABCD with vertices A 2 2 B 2 5 C 2 0 and D 2 3 is a special quadrilateral Select all na hat apply O parallelogram O rectangle O rhombus O square

Find the measure of ZC C B 110 m C 30 D

is the centroid of AABC What is the value of x when GD x 4 and GC 4x 5

Determine the area of triangles given in the area coordinate plane Words to Know Write the letter of the definition next to the matching word as you work through the lesson You may use the glossary to help you parallelogram plane right triangle Determine the area of coordinate plane given in the A a quadrilateral in which both pairs of opposite sides are parallel B a triangle having an interior angle measuring 90 degrees C the amount of space enclosed by a two dimensional figure D a system for locating points in two dimensions that uses a horizontal axis and a vertical axis

14 Determine the volume of water inside the figure to the nearest whole number if it s filled 75 with wate 3 ft 8 ft 4 ft 5 ft RP

Applying the Polygon Interior Angle Sum Theorem An internal angle of a regular polygon has a measure of 140 What type of polygon is it 180 n 2 71 and an 180 n 2 180m 360 140m 40m 360 1 The polygon is a nonagon Exterior Angles of Polygons An exterior angle of a polygon is an M of an adjacent side formed by a side of the polygon

7A 15 Quadrilateral ABCD is shown with the given angle measures Select ALL true statements A Angle A measures 140 degrees B The measure of angle A and D must add to 180 degrees C Angle A measures 55 degrees D Angle D measures 55 degrees E Angle D measures 40 degrees B C A 125 40

Finding the Distance between Two Points in the Coordinate Plane Recall that for any two points x y and x y in the coordinate plane the between them is d x x x y 1 1 x2 1 d 2 1 3 1 3 4 9 16 25 d 5 4 3 2 1 5 4 3 2 1 2 3 4 5 y 45 2 3 4 X

7A 16 Find the measure of the remaining angles of quadrilateral WXYZ X

12 List the volumes from least to greatest 1 Sphere with a radius of 8 in II Cone with a diameter of 6 in and a height of 8 in III Cylinder with a radius of 6 in and a height of 8 in

13 A fish tank in the shape of a rectangular prism has a base with dimensions of 60 inches by 30 inches and a height of 15 inches If the tank is filled with water to a height of 7 5 inches determine the volume of water in the tank

17A 4 The arc from A to 8 NOT passing through C measures 50 degrees Select ALL the true statements A Angle BCA measures 50 degrees 8 Angle BCA measures 25 degrees C Angle BOA measures 50 degrees D The are from B to C not passing through A measures 180 degrees E Angles CBO and CAO are congruent O A

Polygons Polygons are figures formed from three or more line segments such that each segmentintersects exactly two other one at each endpoint and segments with a common endpoint are collinear concave Convex polygon Every line segment connecting any two points on the polygon itself will consistofno points outside the polygon Concave polygon The extension of at least one side or diagonal contains a point on the inside of the polygon N gon is the number of sides

A circle has a center at 4 1 and a point on the circle is located at 2 5 Write the standard form equation that would graph this circle

INDEPENDENT PRACTICE RO 5 Three balls are packaged in a cylindrical container as shown below The balls just touch the top bott sides of the cylinder The diameter of each ball is 13 cm If the diameter of the cylinder is 13 cm what is the volume of the space around the balls

11 A rectangular city with dimensions 10 miles by 11 5 miles is surrounded by a circular region of water with a diameter of 15 miles If the city has a population of 445 312 people determine the population density in the city Round your answer to the nearest whole number O a 3 563 b 3 872 2 836 d 2 061

7 The smaller cone is removed from the larger cone Determine the volume of the figure left over when the larger cone is removed from the smaller cone to the nearest tenth 3 6 12 8

INDEPEND 1 Below are three different shaped cups Which one can hold the most wa 1 cylinder cup with a radius of 8 in and a height of 4 in II rectangular prism cup with a base area of 9 in and height of 6 in III cone cup with a diameter of 12 in and a height of 4 in Iw mo El a

10 The mass of the figure below is 55 lbs Determine the density of the figure to the nearest tenth UNITS 2 in 2015en ort of sugi 13 in

the lines below parallel Use mathematics to support your claim 0 2 4 10

6 A granite block in the shape of a right rectangular prism has dimensions 3 centimeters by 4 centim 5 centimters The block has a density of 28 grams per cubic centimeter What is the mass of the block OF a 168 b 1 680 c 16 800 d 168 000 L units for the mass nogsinnl

9 35 of the figure below is filled with sand What is the volume of sand in the lig 2 m 5m 3 m 6 m 7m

Polygon Exterior Angle Sum Theorem Polygon exterior angle sum theorem The sum of the of the exterior angles of a one ateach vertex is 360 What is the measure of each exterior angle in a regular pentagon Method 1 There are 5 congruentexterior angles 360 Method 2 Use linear pairs 5 Each interior angle has a measure of 108 Using linear pairs we can subtract from 180 180 108 Using the Polygon Exterior Angle Sum Theorem What is the unknown angle measure What is the value of x The sum of the measures of the external angles is 360 90 72 96 82 polygon 360 340 The unknown angle is 20 x 7 20 82 2 linear pair 1 180 3 72 96 5

d Pentagon 3 1 can of paint covers 100 cm Determine the total number of paint cans needed to cover the entire figur below your anst a 12cans b 3 cans C 6 cans d 4 cans 12 6 5

Identify and describe concave polygon Analyze the relationship between angle in a triangle and other polygons convex polygon Prove the polygon interior angle and sum theorems Words to Know Fill in this table as you work through the lesson You may also use the glossary to help you a polygon in which the extension of at contains a point the polygon a polygon in which every line segment Calculate angle measures and solve problems with points on the polygon contains and exterior angles one side any two points outside the polygon

3 10 What is the center and radius of the circle with the equation x y 14x E 14x 12y 4

4 If the figure above is rotated continously about g which of the following 3D figures is formed a Cylinder with a diameter of 6 and a height of 2 b Cylinder with a diameter of 4 and a height of 3 c Cylinder with a diameter of 2 and a height of 3 uns biot d Cylinder with a radius of 3 and a height of 2 AU W 2005 baquila F g dw qua tiba

Polygon Interior Angle Sum Theorem Polygon interior angle num theorem The sum of the measures of the is 180 n 2 where n is the number of the polygon What is the sum of the measures of the interior angles of a pentagon Apentagon has 5 sides son 5 180 5 2 180 3 angles of any n gon Using the Polygon Interior Angle Sum Theorem What is the measure of K Find the sum of all of the interior angles 1800 2 and n 6 180 4 Find the sum of the angle measures that we know of 720 572 J 106 115 154 90 107 Subtract this from the total measure of all interior angle IM Can be divided into 3 triangles 115 M 106 154 K 107 M

Using the Polygon Interior Angle Sum Theorem Regular polygons are both Find the sum the interior angles 180 n 2 and n 5 180 5 2 180 3 This is a regular polygon so all of the angles will be ofequal measure 540 5 Each interior angle measures 108 REAL WORLD CONNCECTION How can you best describe the cells of a honeycomb using polygons What is the sum of the measures of the interior angles of each cell 180 n 2 180 6 2 180 4 and If the polygon is regular what is the measure M 1000 COPIIIII 1000000O necroo000 CORADD600 P 0

Words to Know exterior angle polygon regular polygon an angle formed by a side in a plane a closed figure formed from three or more line segments such that each segment exactly two other segments one at each endpoint and no segments with a common endpointare a polygon that is both of a figure and an extension of an Angle Measures in Triangles What is the measure of C 180 54 85 A 54 and equilateral 85 B

10 The mass UNITSI ed assismlinss 490 E ancianochib 26 cha to soste 90 lugnaben 16ans to 2 The figure below is horizontally cut What is the cross section created a Circle b Triangle c Rectangle 1 Dantagon 16 50 eam sr 17 000 b ons needed to cover the entire figure

Answer Review Key Concepts Polygon interior angle sum theorem The sum of the measures of the 180 1 2 where is the number of angles of any n gon is of the polygon

3 A basketball has a diameter of of the ball is 3 pounds determine the density of the ball 10 lbs cm a 174 5 b 0 006 c 1395 3 d 0 001 lbs cm3 lbs cm lbs cm3 er the em ure

DO NOW 1 Kaliyah and Kennedy were given the task to determine the volume of the figure below Their work is below Analyze their work and determine which student correctly solved for the volume of this figure and identify the other student s error Kaliyah s work 1 V Bh 3 6 15 14 1 3 6 210 V 1 V V 420 ft Kennedy s work 1 V Bh 3 x 1 105X14 14 V 3 1 V 45 14 V 210 ft Which student correctly solve for the volume of this figure What was the other student s error 6 ft 14 ft 15 ft

of water is 1 gram per cm3 An object floats in water if its density is less than water s density and it sinks if its density is greater than water s ass 90 grams is in the shape of a sphere with radius 2 5 centimeters Will the lime sink or float in water Explain or show your reasoning

39 36 S 15 cos R cos S sin R sin S tan R tan S 36 39 15 39 15 39 36 39

E B H G Radius Chord Diameter Secant 1111 AB DF GH CD

Give the value of each trigonometric ratio R 39 36 cos R Cos S sin R S 15 T TIT 15 36 36 39 36 15

5C 6 Draw two solids that are not identical but that have the same volume

5D 7 A cylindrical cup is 8 centimeters in height When filled to the very top it holds 480 cubic centimeters of water What is the radius of the cup rounded to the nearest tenth Explain or show your reasoning

3 5B 3 A superhero action figure has a volume 1500 cm The figure is dilated to create a store display The volume of the dilated figure is 45 000 cm 3 What was the approximate scale factor of the dilation

58 4 A pet supply company makes a small bag that holds 2 pounds of dog food They want to make a bag for large dogs that holds 40 pounds of dog food By approximately what factor will the surface area of the bag increase Round your answer to the nearest tenth

x y 6x 4y 4 0 O Circle 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 N 1 OF 2 3 7 Undo 1 2 3 4 Redo 5 6 x Reset 8 9 10

c sin P Q sin P Q cos Q cos P 2 A satellite s distance above the Earth s surface in km in terms of time in minutes is recorded in the table below 60 232 869 54 48 42 550 869 1000 66 100 24 30 Time min Distance km 6 550 18 12 100 232 36 869 550 232 A number of different equations have been determined and are listed below Equation 1 H t 450 cos 42 550 Equation 3 H t 450 sin t 6 550 a Determine if any of the equations are correct and what error s in the incorrect equations b Determine if other equations can be determined that are not listed already 72 78 232 550 Equation 2 H t 450 cos t 18 550 Equation 4 H t 450 sin t 30 550

TU is tangent to OS What is the value of x S 3x 2 2x 7 U

Consider the graph of a transformed secant shown below 9 8 7 6 y 5 4 y 3 2 1 4 3 2 1 0 1 2 3 4 5 6 7 a What is the period of the corresponding sine graph Show Transcribed Text b What is the amplitude of the corresponding sine graph 2 3 4 5 6 G c What is the midline of the corresponding sine graph d Give a formula for the corresponding sine graph e Give a formula for the cosecant function graphed above

5 Use the following image to answer the questions below 60 120 1 m a Based on the picture what properties can you be sure this figure has Think about angles lines and intersectio b Are I and m parallel Explain your thinking What would you need to do to prove that I and mare parallel