2D Geometry Questions and Answers

1 A student inscribes quadrilateral ABCD inside a circle The measures of angles A B and C are given below Find the measure of each angle of quadrilateral ABCD m A 8x 4 m B 5x 4 m C 7x 4 2 A student inscribes an angle inside a semicircle to form a triangle The measures of the angles that are not the vertex of the inscribed angle are x and 2x 9 Find the measures of all three angles of the triangle Explain how you got your answer

84 a Answer Check nput answer as a b c bo a 78 Co 42 Find the value of the variables For the circle the dot represents the center b 87 36 nput answer as a b c

Find the value of x to the nearest tenth X 4 2 10

23 m 4 5x m 5 4 x 5 24 m 2 4x 3 m27 5 x 3 25 m 3 1 26 m 1 m25 x 52 II 35 3 5 6 7 8 4 N Exercises 23 30

D Exercises 17 18 18 Given Find AB DC DB bisects LADC m 1 36 m A

1 m A 63 and m B 42 2 m B 39 and m C 820 3 mA m C 57 4 m B 42 and m A m C A Exercises 1 6 03 B

In Exercises 13 to 15 j k and AABC 13 Given m3 L 1 50 m 4 72 m 1 m2 and m25 Find m B A 5 6 3 4 Exercises 13 15 2 1 C

In Exercises 9 and 10 classify the triangle not shown by considering the measures of its angles 9 a All angles of ABC measure 60 b In ADEF mLD 40 and m E 50 10 a In AXYZ m X 123 b In ARST m R 45 m S 65 and m T 70

8 a In AXYZ XY YZ b In ARST RS 6 ST 7 and RT 1 8

houses at points R and T in front of the plane With angle measures as indicated find m R 12 000 37 65 R 37 On a map three Los Angeles suburbs are located at points N Newport Beach P Pomona and B Burbank With angle measures as indicated deter mine m N and m P 8 The roofline of a house shows the shape of right triangle ABC with m C 90 If the mea of C B 33 X 2x N

15 Does the relation is complementary to for angles have a reflexive property consider one angle A symmetric property consider two angles A transitive property consider three angles

c transitive property consider coplanar lines m n and g 6 In a plane 1 m and t 1 m By appearance how are e and related

4 If m 4 110 8 find a m S b m 8 EY l 1 2 3 4 5 6 7 8

7 With respect to b as a transversal for lines a and c a which angle corresponds to Z2 b which angle is the alternate interior angle for Z6 8 With respect to c as a transversal for lines a and b a which angle 12 5 6 10 9X11 12 Exercises 7 8 3 7 8 corresponds to 25 b which angle is the alternate exterior angle for 4 a b

15 m with transversal t and 00 bisects LMON If m 1 112 find the following a m 2 b m 4 c m 5 d m MOQ 16 Given Find 17 Given Find e m Transversal t m 1 4x 2 m 6 4x 2 x and m 5 m n Transversal k m 3 x 3x m 6 x and m 4 x 4 x 5 EY m l 6 3 LO 1 2 M 4 At 5 0 7 I Exercises 15 16 6 N

In Exercises 27 to 35 complete the formal proof of each theorem 27 If two angles are complementary to the same angle ther these angles are congruent Given Prove 21 is complementary to 23 22 is complementary to 23 21 42

Given Find Given Find m n Transversal k m 3 x 3x m 6 x and m 4 m n Transversal k m 1 m 2 m 8 x 4 x 5 5x y 3x y 3x 5y x y and m 8 m 2 1 4 n 3 Exercises 17 19 6 LO 5 8 7

3 If two angles are supplementary to the same angle then these angles are congruent Given 1 is supplementary to 22 23 is supplementary to 22 21 43 Prove HINT See Exercise 27 for help 2 3

In Exercises 19 to 26 use the drawing in which AC intersects DB at point O A 19 If m 1 125 find m2 m 3 and m 4 20 If m 2 47 find m 1 m 3 and m 4 21 If m 1 3x 10 and m 3 4x 30 find x and m 1 D 3 O 1 2 4 B C

19 Sometimes symbols and abbreviations are used in place of a word or phrase What word or phrase is represented or abbreviated by each of the following b Zs c supp d rt a I e m 1

In Exercises 1 to 6 state the hypothesis H and the conclusion C for each statement 1 If a line segment is bisected then each of the equal segments has half the length of the original segment

3 Does the relation is perpendicular to have a reflexive prop erty consider line A symmetric property consider lines and m A transitive property consider lines l m and n

Is the following equation linear and con x 13y 3 17

lows The length of a line segment equals the sum of the lengths of its parts State a general conclusion regarding AB based on the following figure

Find the equation of the the line satisfying the given conditions Through 2 3 perpendicular to a second line y x O y x Oy x Oy x O y x

Solve 5 sin 5x 4 for the two smallest positive solutions A and B with A B A B Give your answers accurate to at least two decimal places

12 Given Prove 3 2 Statements 1 41 23 2 and 4 21 22 23 24 Ls 2 and 3 are complementary Ls 1 and 4 are complementary 221 3 3 Ls 2 and 3 are complementary 6 42 and 24 2 4 5 mZ1 m24 90 PROOF 1 Reasons 2 If two Ls are then their measures are equal 3 4 The sum of the measures of complementary Zs is 90 5 6 If the sum of the mea sures of two angles is 90 than th

In Exercises 11 to 22 use the Given information to draw a conclusion based on the stated property or definition A Exercises 11 12 11 Given 12 Given 13 Given 14 Given 15 Given M 16 Given B A M B Segment Addition Postulate M is the midpoint of AB definition of midpoint I m 1 m 2 defini tion of angle bisector EG bisects LDEF defi nition of angle bisector Ls 1 and 2 are comple mentary definition of complementary angles 90 m 1 m2 definition of D E 1 2 G F Exercises 13 16

In Exercises 27 to 30 fill in the missing reasons for each geometric proof 27 Given Prove D E F on DF DE DF EF PROOF Statements 28 Given Prove 1 D E F on DF 2 DE EF DF 3 DE DF EF Statements 1 E is the midpoint of DF 2 DE EF 3 DE EF DF 4 DE DE DF 5 2 DE DF 6 DE DR E is the midpoint of DF DE DF 1 2 3 PROOF D E Exercises 27 28 1 2 3 4 5 Reasons Reasons F

36 Given Construct Straight LDEF A right angle with vertex at E HINT Use Construction 4 E

37 Given that a b and c 0 which is correct ac bc or ac bc

In Exercises 7 to 10 state the property or definition tha justifies the conclusion the then clause 7 Given that Ls 1 and 2 are supplementary then m 1 m22 180 R

28 For two complementary angles find an expression for the measure of the second angle if the measure of the first is a x b 3x 12 c 2x 5y

In Exercises 1 to 6 which property justifies the conclusion of the statement 1 If 2x 12 then x 6 2 If x x 12 then 2x 12

15 Using variables x and y write an equation that expresses the fact that 1 and 2 are a complementary b vertical

A company is going to make a water tank in the shape of a cylinder As shown below the tank will have a height of 4 ft and a diameter of 10 ft The tank will be made from metal including its top and bottom Suppose the total cost of the metal will be 9325 80 How much will the metal cost per square foot Use 3 14 for and do not round your answer 10 ft 4 ft 0 X

rallelogram KLMN is shown below Give the coordinates of K L 0 s M 1 0 K N u 0 x K

Find the perimeter of the parallelogram with these vertices 6 4 1 4 1 5 6 5 Give an exact answer not a decimal approximation Simplify your answer as much as possible Scratch Area Not Part of Answer d 1 Perimeter 24 3 7 X

Compare the given measures by choosing or If there is not enough information select Cannot be determined If necessary you may learn what the markings on a figure indicate A X E K 15 Y 92 8 H 9 L 41 7 D B P 15 F 22 61 e 8 C G OAD CD Cannot be determined O mLF mLY O Cannot be determined KL QR Cannot be determined X 3

Write an equation of the circle with center 8 3 and radius 5 0 00 0 0

A designer builds a model of a bicycle The finished model is exactly the same shape as the original but smaller The scale factor is 2 9 a Find the ratio of the surface area of the model to the surface area of the original b Find the ratio of the height of the model to the height of the original c Find the ratio of the volume of the model to the volume of the original Write these ratios in the format m n surface area height volume X

Here are the endpoints of the segments JK MN and PQ J 4 5 K 7 7 M 1 6 N 1 3 P 3 0 Q 5 3 Follow the directions below a Find the length of each segment Give an exact answer not a decimal approximation JK MN 0 PQ b Check all statements that are true below OJK MN OJK PQ OMNPQ None of these are true 4 9 16 9 8 08 X S

Determine if the statement is true or false The function defined by g x 3 x 3 2x 1 touches but does not cross the x axis at True False X at 1 0 5

Find x Round your answer to the nearest tenth of a degree 18 11 X 0

The empty gas tank of a truck needs to be completely filled The tank is shaped like a cylinder that is 3 5 ft long with a diameter of 2 4 ft Suppose gas is poured into the tank at a rate of 1 7 ft per minute How many minutes does it take to fill the empty tank Use the value 3 14 for it and round your answer to the nearest minute Do not round any intermediate computations minute s X

A company rents water tanks shaped like cylinders Each tank has a diameter of 12 feet and a height of 3 feet The cost is 2 per cubic foot How much does it cost to rent one water tank Use 3 14 for and do not round your answer

For the following right triangle find the side length x X

In the figure below n g Find the values of x and y 5y 74 84 to X 11 11 y 0

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

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