2D Geometry Questions and Answers

1 point A circle has a diameter of 10 centimeters If a sector with a central angle of 50 degrees is cut out what is the area of this sector 5 46 square centimeters 10 91 square centimeters 3 14 square centimeters 43 63 square centimeters

What shape is formed when a plane slices through a sphere at any angle triangle circle rectangle oval

1 point Arc length is a fraction of a circle s Odiameter area circumference Oaxis

1 point You are pouring juice into a cylindrical cup with a 2 inch radius and height of 8 inches If you want to fill it exactly half full how many cubic inches of juice should you pour in 100 6 cubic inches 25 13 cubic inches 50 3 cubic inches 16 cubic inches J

A plane slices through a rectangular pyramid parallel to the base What is the shape of the cross section circle rectangle 00 square triangle

A circle has a diameter of 10 centimeters If a sector with a central angle of 50 degrees is cut out what is the area of this sector 5 46 square centimeters 10 91 square centimeters 43 63 square centimeters 3 14 square centimeters

A hula hoop has a radius of 19 inches What is the length of the arc subtending 1 4 of the hoop 14 9 inches 43 8 inches 29 8 inches 59 7 inches

Which of the following vectors are normal to the surface z 2 2x y at the point 1 1 1 Select one or mo O 4i2j3k O 4i 2j 3k O4i 2j 3k O 4i 2j 3k

10 10 0 10 20 In the hyperbola above the center is 10 The slope of the Asympototes is 4 20

Question 3 Points 2 Find the measure of angle 0 in the given triangle M 25 cm O 33 59 O 44 56 30 cm O 56 24 0 N

Identify the similar right triangles from the given choices O 10 7 07 F R 14 ASA Z 39 12 15 Q X 5 9 5 4A 15 A 3 C 7 8 C 36 P E A A 9 5 11 13 Y D 5 E

Question 7 Find ZDCE given that AB CD B28 O 72 O 28 O 90 Points 1 62 E D

Question 7 The given two right triangles are similar when X A X O 12 O 15 O 36 O 39 C Points 2 39 15 12 BD F 5 13 E

Question 2 Points 3 Which of the following is true about similar right triangles O Corresponding angles are not equal O Corresponding trigonometric ratios are in proportion O Corresponding trigonometric ratios are equal O Corresponding sides are equal

Question 1 Find the measure of the angle 0 in the given right triangle A 20 Points 3 B 40 0 30 O 0 20 8 25 0 45 8 C

Find the vertices and foci of the following ellipse 1 5 Select one O a Vertices 0 3 Foci 0 2 O b Vertices 0 2 Foci 0 3 O c Vertices 3 0 Foci 2 0 O d Vertices 2 0 Foci 3 0

Question 6 Which triangle is not similar to any of the other three triangles 57 83 A OA OB OC Points 2 B 40 57 40 C 83 40 D 67

Question 10 If the given triangles are similar find the missing length T V O 36 O24 O 15 C Points 2 27 45 U X 3 Y 4 N 5

Question 4 The given two right triangles are similar when X F 4 B A X O 10 3 CE 08 Points 2 07 05 24 18 30 G

The major axis of the following ellipse x 5 16 y 2 36 axis of length is the and the minor axis is the with length

Question 8 Points 1 Length of a segment XY is 32 m Find the measure of the dilation image for a scale factor of 3 20 m O24 m 25 m 28 m

Find the measure of angle AEC E A O 41 90 49 45 D B 41

Question 4 If a triangle is dilated with a scale factor of k then the measures of the dilated triangle are obtained by multiplying the measures of the original triangle by OK 1 Ok O k 1 Points 1 Ok

Question 3 Points 1 Find the length of the base of the new triangle after reduction by a scale factor of if it originally measures 9 inches O4 inches O3 inches 3 33 inches 2 5 inches

Question 2 Triangles ABC and XYZ are similar In AABC ABC 35 and BCA 80 Find ZXY 80 65 O 115 Points 2 100

Question 1 Points 1 A triangle is dilated with a scale factor of 3 Then the corresponding angles are O congruent O decreased by 3 O increased by 3 O increased by 3 times

Using the complete the square method find the center and radius of the equation x 2x y 18y 57 Center Radius

Find the vertex of the following parabola x y 10y 26 Select one O a 1 5 O b OC O d 1 5 None of these 1 5

Find the vertex of the given equation of the parabola x 2 8 y 3 Select one O a 2 3 O b 2 3 OC 2 3 O d 2 3

Which of the folllgraph of the equation of the following hyperbola indicating vertices foci and asymp 144 Select one a O b O C O d 0 2 2 0 2 0 2 0 2 2 y x 13 0 2 1 12 0 2 2 0 4 0 4 0 0 2 13 X 0 2 13 12 5 2 6 1 3 2 6 1 2 15 1 12 0 6 4 y x 13 0

The line y mx c intersects the circle x y a a maximum of 2 Select one O a 3 O b 2 O C 1 O d 4 points

Which is the graph of the circle x y 10x 8y 5 0 Select one O a O b 10 10 10 10 20 5 10 10 5 0 20

1 Which inequality is represented by the following graph OC y 3x 2 OA y 3x 1 OD y 2x 1 5 B y 2x 3 O ry 2 3

Jan is constructing an inscribed circle in a triangle What is the center of this circle called orthocenter centroid circumcenter incenter

Which of the following is NOT true of a perpendicular bisector it bisects a segment to construct it we have to draw two arcs using each of the endpoints as centers to construct it we have to draw two arcs using the intersection points as centers it forms a right angle with the segment

the line passeng through your answer Dietermine the slope of the given points worite exact simplified form 212 615 and 7 2 2 5

1 point D C B If the measure of arc AB is 64 degrees what is the measure of angle ADB 128 degrees 32 degrees 90 degrees 64 degrees

1 point A Solve for x x 5 O x 10 x 2 x 4 42 10 E B X D

E 00 11 D 43 45 Is segment CE tangent to circle D Why or why not No this doesn t look like a right triangle Therefore the segment is not tangent by the converse of the Perpendicular Tangent Theorem Yes this looks like a right triangle Therefore the segment is a tangent by the converse of the Perpendicular Tangent Theorem Yes the Pythagorean Theorem holds true so it is a aright angle Therefore the segment is a tangent by the converse of the Perpendicular Tangent T e converse of the Perpendicular Ta No Pythagorean theorem does not hold true so it s not a right angle Therefore the segment is not tangent by t

33 35 24 24 A X 24 8 2 45 y 10 X 34 36 d 60 C 3 Fe Jo a 24

0 1 point Nate is constructing a tangent line to a circle he drew from a point outside the circle Once he has the circle and the point drawn what is his next step connect the center of the circle to the point outside the circle label the points where the arc intersects the circle construct a perpendicular bisector construct rays from the point through the points of intersection

1 point Which of the following constructions must you know how to do in order to construct a circumscribed circle for a given triangle duplicating a line segment angle bisector inscribed quadrilateral perpendicular bisector

1 point Laurie is constructing an angle bisector She sketched her angle then opened her compass to a radius length less than the length of the rays that make up the angle What should be her next step draw an arc using the vertex as the center draw a ray from the point of intersection to the vertex label the point of intersection of the two arcs mark the points of intersection

b If a 11 solve for b and c b 11 3 c 22 Ob 11 c 11 2 b 11 c 22 b 5 5 c 11

Given any two side lengths in a right triangle what is used to find the third side length sine tangent Pythagorean Theorem cosine

1 point A meteorologist measures the angle of elevation to her weather balloon as 33 degrees A radio signal from the balloon indicates that it is 1601 meters diagonally from her location How high is the weather balloon above the ground Round to the nearest hundredth 1342 71 feet 871 97 feet 1039 70 feet

Solve for u an 4 O A OB V 30 2 U A u 8 v 6 v 6 B u 4 C u 4 D u 8 v 23 v 2 3

An ellipsoid is a 3D shape whose cross sections are ellipses A whispering gallery is a room with a half ellipsoid ceiling If one person whispers from one focus another person can hear them clearly from the other focus Suppose a whispering gallery has 5 foot walls A cross section of the ceiling can be modeled by the ellipse shown below centered at the origin with a horizontal major axis If the maximum height of the ceiling is 20 ft and the width of the room is 50 ft write the equation of the ellipse 201 50 5

A circle of radius 12 units is divided into 8 congruent slices 1 What is the area of each slice 2 What is the arc length of each slice square units T units

point In a basketball drill two players start at the same spot on the court One player runs 6 feet down the court and the other player runs 4 5 feet across the court in a direction perpendicular to the first player What is the distance that one player must pass the ball for it to reach the other 6 5 feet 7 5 feet 4 feet 8 feet Da