2D Geometry Questions and Answers

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3MK 24 JL 20 and m2MJL 50 K M W L NK NL ML JM m2KNL m2KJL m2MLK m JKM m2JML

In AABC m C 45 If point D is the midpoint of AB and point E is the midpoint of BC what is the measure of ZADE

Find the reference angle create a triangle and find all angles and sides of the triangle Consider the hypotenuse of your triangle 1 unit 5 7 290 et 715 X 6 8 240 380 X 0803

Part A eflect G and F across the line x 7 Label the images with prime notation Then draw quadrilateral GG F F 10 G 10 Part B Give the most precise name for quadrilateral GG F F Explain WHY IT IS the figure you named by explaining how it meets the definition of the figure The most precise name for the figure is because

Find the length of side x Round to the nearest tenth X 6 5 X 68 5

What is a sequence of transformation to describe the figures in the graph 10F 8 C B A 864 2 2 A 2 4 6 B 8 10 Rotate 90 clockwise about the origin then Reflect over the y axis Rotate 270 counterclockwise about the origin then Reflect over y x Translate right 2 then Reflect over the y axis Reflect over the y axis then Translate right 2

Toets H3 Wortels Opgave 1 6 punten Schrijf zo kort mogelijk en vereenvoudig indien mogelijk je a 4 2 3 2 5 b 2 3 3 9 c 3 3 2 12 d 3 12 27 e 7 2 3 Opgave 2 5 punten Schrijf de wortels als een wortel met alleen een getal onder wortelteken C 2 13 a b 5 3 2 5 Vereenvoudig indien mogelijk d 2 90 e 3 50 f10 8 Opgave 3 5 punten In de figuur zijn alle hoeken recht a Bereken de omtrek van de figuur Geef een zo kort mogelijk antwoord 2 2 3 6

Solve for x Round your answer to the nearest tenth 70 T 6

16 A line segment has endpoints 2 7 and 5 4 The line segment is dilated by a factor of 3 around 4 3 What are the new endpoints and length of the line segment

4 Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of 0 where 0 x 25x 36 5x 6tan

1 Hints All trapezoids have two pairs of consecutive supplementary angles Trapezoid Property All trapezoids have at least one pair of parallel sides Isosceles Trapezoid Property Sides All isosceles trapezoids have at least 1 pair of opposite congruent sides legs Isosceles Trapezoid Property Angles All isosceles trapezoids have 2 pair s of consecutive congruent angles Isosceles Trapezoid Property Diagonals The diagonals of all isosceles trapezoids are congruent P Triangle Angle Sum 180 Alternate Interior Angle Theorem T 76 34 R 73 410 A Vertical Angle Theorem Same Side Interior Angle Theorem 2 P 21 97 45 65 thir an Isosceles Trapezoid Yes or No agonal Is this an Isosceles Trapezoid Yes or No

Rectangle AE mLABD m2DAE A 20 EB 5m MLADE mzBAC B Woled Caugh audmona Square to cemuzeem D DE mLABD mLACD 7m AE C mLAED m DBC

Find the missing side lengths and angle measures indicated for the figures below Parallelogram D mLABD A EB 725 mLDAC 30 35 7 cm E 72 5 72 6 cm AE 35 m2ACD 80 MLADB Rhombus EB mLABD m2BAE D 30 9 cm 46 cm C AE B m AEB MLADE

Find all missing side lengths and angle measures of the figures below Parallelogram Rectangle 71 8 cm 10 ft 3 cm GOAsin HW 4 ft Rhombus Square Thurs 4 cm 5 m 101

State the most specific name for each figure or 1 3 5 7 30AM 3A8AM 2 4 6 8

5 P P T 24 6 cm TC 3 cm 310 AC 8 cm A s this an Isosceles Trapezoid Yes or No 6 RA 9 cm P 270 T 11 cm TC 18 6 cm R AC A Is this an Isosceles Trapezoid Yes or No

T P 50 R 34 26 A s this an Isosceles Trapezoid Yes or No 4 T P46 R 940 26 A Is this an Isosceles Trapezoid Yes or No

34 f x x 5x 6 4x 4 48 6 4 2 8 6f 4 2 2 61 8 6 X

that describes plotting points with polar coordinates Click here to watch the video Plot the point 3 150 Then find the rectangular coordinates of the given point Choose the graph of 3 150 below OA OB 180 O C 180 90 270 90 0 0 180 O D 180 90 270 90 0 0 Q A

14 In the following diagram x and y represent adjacent sides of a parallelogram Does x y x Explain A B y D

What is the image of the point 6 2 after a rotation of 90 counterclockwise about the origin

For each figure determine how many lines of reflection and how many angles of rotation will carry the figure onto itself B

Solve for x 15 2r 4 18 8

Complete the following problems after the mini lesson CD bisects C Solve for CA D 11 22 B

Tyler says that since triangle ACD is similar to triangle ABC the length of CB is 11 96 Noah says that since ABC is a right triangle we can use the Pythagorean Theorem So the length of CB is 12 exactly Do you agree with either of them Explain or show your reasoning AD 5 4 6 13 B

Next draw CD perpendicular to AB as shown in the next figure Label the red triangle as triangle 2 The blue triangle as triangle 3 How many triangles do you see in the figure Why are the three triangles similar to each other

a Determine if each transformation represents a translation rotation reflection or none CC D How I know b A B 7 A How I know B C C A A B B 02 How I know C

Symmetry For each figure determine how many lines of reflection and how many angles of rotation will carry the figure onto itself B

1 3 2 4 8 60 10 7 9 11 5 59 6 m21 m 2 m23 m24 m25 m26 m27 m28 m 9 m 10 m 11

As shown in the figure AABC satisfies ZABC 30 AB 4 take the circumcenter of AABC as the center to make a circle I AABC is within I extend AB to intersect I at D extend BC to intersect I at E if BD 6 CE 5 find the area of T E A B D

9 Find the slope of the tangent line to the polar curve r when 0

21 Given C 119 B 42 and c 15 use the Law of Sines to solve the triangle for the value of a Round your answer to two decimal places a 7 3 O a 6 81 O a 4 36 O a 19 61 a 5 58

12 Determine the area of a triangle having the following measurements Round your answer to two decimal place B 84 38 a 7 and c 8 22 30 sq units 27 88 sq units 25 09 sq units 33 45 sq units

Use the law of Cosines to solve the given triangle Round your answer to two decimal places a 9 b 4 5 C 110 b C a B

ladder of length 10 ft has a distance of 6 ft from a wall To what height does the ladder reach wall 10 ft ladder 6 ft O 1 8 ft O 2 60 ft O 3 16 ft 4 4 ft

Consider the following sin 10 cos 0 a Eliminate the parameter to find a Cartesian equation that represents the curve 2 F Cloudy X sin CHOICE A b Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases CHOICE B 0 CHOICE C y 0 0 5 0 5 y 0 2 0 4 0 6 0 8 1 0 y 0 2 0 4 0 6 0 8 TE SOST 1 0 0 5 0 5 Q Search X 1 0 CHOICE D 1 0 0 5 0 5 y 1 0 0 8 0 6 0 4 0 2 0 8 0 6 0 4 0 2 0 5 0 5 1 0 1 0 A

10 Consider the function y 3 x 2 8 a State the transformations the b Graph the parent function c Graph the transformed function 1K Show your work in the table below or graph all the transformations on the grid provided In 8

In Exercises 5 8 determine which lines if any must be parallel Explain your reasoning 5 6 7 8 p HI p Am Am n n 1 2 S a k t

12 in 45 a 30 b zoom in 4 4 X given this triangle Find a and b given this triangle You can format your answer like a 38 in b 5 13 radical 17 if you cannot find how to enter radicals on your chromebook Include units in at the end of each answer a 5 b 7

16 A line segment has endpoints 2 7 and 5 4 The line segment is dilated by a factor of 3 around 4 3 What are the new endpoints and length of the line segment 17 P State whether the two triangles are similar and explain why T 100 45 100 R s 35 U 18 Given line m and point 0 not on line m The image of line m is constructed through a dilation centered at 0 with a scale factor of 3 Which of the following statements best describes the image of line m a line passing though point 0 c a line parallel to line m b a line intersecting with line m d a line perpendicular to line m

21 In Triangle PQR if PR is extended through R to T If QPR 3x 6 and PQR 2x 6 and QRT 150 degrees Find the value of x

e cos sin 3 f cos tan

9 Evaluate each of the following a sin 2 b arccos 2

5 sin x cos x 1 0 x

8 Triangle A B C is the image of ABC after a dilation of 2 Which statement is true a AB A B b BC 2 B C c mzB mzB d mA 1 2 m A

6 What will be the coordinates of point R if figure PQR is reflected across the y axis 6 3 2 1 5 3 2 3

9 Line segment AB is shown in the diagram below Which two sets of construction marks lobeled I II III and IV are part of the construction of the perpendicular bisector of line segment AB X IV oll and II b I and III c II and t d Il and iv X 2 ac i 90 degl