2D Geometry Questions and Answers

Identify the acidic and basic amino acids in the active site in the given diagram Drag the appropriate amino acids to their respective bins Acidic CH 2 c 0 NH H N Basic CH CH OH CH COO H N Neutral CH 3 NH NH Reset Help

O Lesson 1 4 Checkpoint Once you have completed the above problems and checked your solutions complete the Lesson Checkpoint below Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 20RS and ZSRQ are a linear pair If mLORS mSRQ 3x 6 find x ST poin R PO Getting there Q If the Illuminate growth benchmark is completed during this LEP check the box to the right Got it

1 The two angles are supplementary angles If m21 45 then what is the measure of 22

29 Determine whether the dilation from Figure A to Figure B is a reduction or an enlargement Then find its scale factor 30 y B k 1 Logo H gaits y A B

2 Visualize diagram the face of a traditional clock displaying the time 3 30 pm Precisely how many degrees exist between the hour hand minute hand

Use the figure below to find only one angle that fits each description 7 m212 8 m 12 9 m 12 10 m 12 because of corresponding angles because of alternate interior angles sumitno12 tical angles 10 5 6 because of vertical 180 because of consecutive angles 9 10 13 14 HB 3 4 seanl 7 8 ried 11 12 15 16

Find the missing term 19 1 1 2 3 5 8 21 Draw the next shape in each pattern 20

5 How many lines of reflection symmetry does the design below have Show your thinking LS Clishib

Find the lengths x and y in the figure below y 22 3 16 5 16

Sketch label and mark the figure described below 11 Isosceles right triangle ABC with AM where M is the midpoint of base BC SSF 12 True or False If the side of an octagon has length 3 cm then its perimeter is 24 cm

Solve for the variables Figures may not be drawn to scale 5 3x 8 2x 12 1300

11 In a computer catalog a computer monitor is listed as being 19 inches This distance is the diagonal distance across the screen If the screen measures 10 inches in height what is the actual width of the screen to the nearest inch 10

Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION sin 0 cos 0 5 sin 8 0 0 MY NOW

Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter tan 0 9 2 cos 0 1 0 0

Find all solutions of the given equation Enter your answers as a comma separated list Let k be any integer Round terms to two decimal places where appropriate 4 cos 8 3 0 0 rad

Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to two decimal places where appropriate sin 0 1 8 rad

Prove the identity cos 2x sin 2x cos 4x Use a Double Angle Formula and simplify cos 2x sin 2x cos 2 11

Prove the identity sin x cos x 1 sin 2x Expand the product and use a Pythagorean Identity and a Double Angle Formula to simplify sin x cos x sin x 2 sin x cos x 1 2 sin x

Simplify the expression by using a Double Angle Formula or a Half Angle Formula a 2 tan 4 1 tan 4 b 2 tan 40 1 tan 40

Prove the identity sin 10x 2 sin 5x cos 5x

A right triangle has legs with lengths of 28 centimeters and 20 centimeters What is the length of this triangle s hypotenuse in centimeters A 8 6 B 4 74 C 48 D 1 184 6 The perimeter of an isosceles triangle is 83 inches Each of the two congruent sides of the triangle has a length of 21 inches What is the length in inches of the third side 7 In a right triangle the measure of one of the acute angles is 51 What is the measure in degrees of the other acute angle A 6 B 39 19 D 31 8 Each side of a 30 sided polygon has one of three lengths The number of sides with length 8 centimeters cm is 5 times the number of sides n with length 3 cm There are 6 sides with length 4 cm Which equation must be true for the value of n A 5n 6 30 B 6n 6 30 C 8n 3n 4n 30 D 8 5n 3m 4 6 30 9 A right circular cone has a height of 22 centimeters cm and a base with a diameter of 6 cm The volume of this cone is n cm What is the value of n

Name Date Carefully read and respond to each question You will be taking the PSAT on Tuesday 10 24 2023 References 1 A 70 B 140 C 1 156 D 1 224 A C 2pr V fwh A w A 8 B 16 C 64 D 128 V nr h h What is the area in square centimeters of a rectangle with a length of 36 centimeters and a width of 34 centimeters 2 There are 170 blocks in a container Of these blocks 10 are green How many blocks in the container are green 3 The area of a square is 64 square inches What is the side length in inches of this square a The number of degrees of arc in a circle is 360 The number of radians of arc in a circle is 2 The sum of the measures in degrees of the angles of a triangle is 180 2x 60 2 30 4 A right rectangular prism has a length of 28 centimeters cm a width of 15 cm and a height What is the surface area in cm of the V h 2 45 S x 3 Special Right Triangles Perioa V v wh

O Find the value of x 16x 4 9x 6 58

If we want the median of these five numbers to be 45 what number belongs in the blank If nothing will work just type NOT POSSIBLE 25 90 10 60

Find the number of integer values of BC x 8 A D

Use a graphing utility to determine which of the six trigonometric functions is equal to the expression Verify your answer algebraically 1 1 sin 0 cos 8 cos 0 1 sin 0

2 2x 3 For the function F x X domain and range and c use the final graph to list any vertical horizontal or oblique asymptotes a graph the rational function using transformations b use the final graph to find 17 2 a Which of the following transformations is required to graph the given function 1 OA Shift the graph of y 3 units to the left and shift it 2 units up 2 x O B Vertically stretch the graph of y by a factor of 3 reflect it about the x axis and shift it 2 units down X OC Vertically stretch the graph of y by a factor of 3 reflect it about the y axis and shift it 2 units up X Vertically stretch the graph of y hy a factor of 3 reflect it about the x avis and shift it 2 units un

Use the graph shown to find the following a The domain and range of the function b The intercepts if any c Horizontal asymptotes if any d Vertical asymptotes if any e Oblique asymptotes if any MIDD 9 6 3 Q Find the vertical asymptotes if there are any Select the correct choice below and fill in any answer boxes within your choice O A x Type an integer or a simplified fraction Use a comma to separate answers as needed OB There are no vertical asymptotes Find the oblique asymptotes if there are any Select the correct choice below and fill in any answer boxes withi

4 For the function H x a graph the rational function using transformations b use the final graph to find the X 2 domain and range and c use the final graph to list any vertical horizontal or oblique asymptotes a Choose the correct graph below O A B Q O C Q D

Use the graph shown to find the following a The domain and range of the function b The intercepts if any c Horizontal asymptotes if any d Vertical asymptotes if any e Oblique asymptotes if any C 9 6 Find the y intercepts if there are any Select the correct choice below and fill in any answer boxes within your choice O A y Type an integer or a simplified fraction Use a comma to separate answers as needed

15 Solve a system of equations to find the values of x and y Show all work y 30 4x 3x 2y 9 0 waled sugit ani or

2 If mLABD 39 and m2DBC 22 what is mLABC Draw two angle pairs that will justify your answer

15 m 2 x 94 2 H H

120 11

Name A lighthouse that is 50 meters above sea level marks the entrance to a bay The lighthouse is used to orient ships as well as to provide a lookout point for the local coast guard 50 m a A pair of ocean kayakers estimate their distance to the entrance of the bay using the lighthouse They measure the angle of elevation from their position to the top of the lighthouse to be about 16 Draw a diagram showing the kayaks in relation to the lighthouse illustrating the angle of elevation b Knowing the height of the lighthouse and the angle of elevation from the kayakers to the top of the lighthouse calculate the kayakers distance to the entrance of the bay c A member of the coast guard is on lookout at the top of the lighthouse She spots a distress signal from a boat She measures t angle of depression to the boat to be 8 Draw a diagram showing the boat in relation to the lighthouse illustrating the angle c depression d Knowing the height of the lighthouse and the angle of depression from the top of the lighthouse to the boat in distress calc the distance from the lighthouse to the boat

Find the length of LM K LM 16 N 10 12 L M 0 Write your answer as a whole number or a decima

V is the midpoint of UW and S is the midpoint of TW If TU z and SV 2z 45 what is the value of z W V S

R is the midpoint of QS and U is the midpoint of QT If ST p 53 and RU p 4 what is the value of p Q S R U

QS is a midsegment of APRT If PT v 22 and QS v 7 what is the value of v T S P Q R 20

RT is a midsegment of ASUV If UV y 6 and RT 2y what is the value of y S R V T U

Determine what ADDITIONAL INFORMATION would be necessary to prove the two congruent using the suggested postulate or theorem with the given information NC RO NC RO 13 Given ZN ZV and NG VI Use SAS Postulate Mark the pairs of sides and angles that you use complete the congruence between the triangles and choose SSS SAS ASA AAS or HL as the reason 15 ANCO A by 14 Given VK LIK NS L GS and ZV ZN Use ASA Theorem THE SN HNAK THINS 17 ATHA A 19 APIE A P is the midpoint of IS IE ES H by by O E 16 AKGI A ZK ZN GI bisects ZKGN 18 AGIVA GV bisects LIGE GV bisects LIVE 20 ATEUA TE TR ZTUE ZTYR by K by G by G I U K N

bel AMNO and AXYZ Indicate the additional pairs of corresponding parts that would have to be proved congruent in order to use the given postulate or theorem to prove the triangles congruent 8 9 ZNLY and NO YZ by ASA V 20 ZZ and ZM ZX by AAS 10 ZNZY and ZM ZX by ASA 11 Given AABC ADEF AB 15 BC 20 AC 25 and FE 3x 7 find x 12 Given AABC ADEF DE 10 EF 13 DF 16 and AC 4x 8 find x

Then identify the transformation Graph the Image R S T to check on to write the rule that maps each preimage to its your answer The coordinate rule is The transformation is Preimage P 4 2 Q 1 3 R 3 3 P Q R Image Preimage R 4 3 S 1 3 T 4 1 Bike Image R 1 1 S 4 1 T 1 3 R 2 Draw the image of each figure under the given transformation Record the coordinate of the Image P Q R on th table sty x y x 1 y 2 P t 5 R S 0 O 5 S

P HW 0000 7 1 Which of the following translations is needed to carry preimage ARST to its image AR S T 5 Q 0 ework Complete problems 1 8 for independent practice 3 Write the coordinate rule to carry APQR onto its image AP Q R A x y x 3 y 4 B x y x 4 y 3 C x y x 5 y 3 D x y x 5 y 3 TP dent Practice The coordinate rule is When you are finished check the solutions with your teacher Q 2 Which of the following translations is needed to carry preimage AJK to its image Al J K T 0000 A x y x 2 Y 2 B x y x 2 y 3 C x y x 2 y 2 D x y x 3 y 3 4 RST maps to AR S T Preimage R 1 1 S 1 1 T 2 2 The coordinate rule is K The transformation is Image R 3 2 S 3 2 T 6 4 The crime famstur

For Your Turn 2 3 write the coordinate rule that maps each Preimage to its Image Then identify the transformation Record the Preimage and Image on the graph 2 is partly done for you 2 AABC maps to AA B C Preimage A 2 6 B 2 6 C 2 3 The coordinate rule is x y 2x y The transformation is Dilation with a horizontal stretch by a factor of 2 and a vertical compression by a factor of 3 ARST maps to AR S T Preimage R 2 1 S 2 1 T 4 2 The coordinate rule is Image A 4 2 B 4 2 C 4 1 The transformation is Image R 1 3 S 1 3 T 2 6 0 5 0 75 5

1 Draw the image of each figure under the given transformation Record the coordinate of the Image K L M on the table 5 x y x y Preimage K 2 1 L 4 3 M 2 4 K L M Image K M 16

3 Write the coordinate rule to carry AABC onto its image AA B C 5 A A 4 OC C B 5 B 5 The coordinate rule is EXPLAIN 2 15701 Need help Visit the L4L Math Resources We to find videos and other resource Describing Nonrigid Mot Notation Read Explain 2 and complete Your Turn 1 3 adapted from Lesso There are some transformations that preserve the figure s length sha transformations that do not A nonrigid motion is a transformation th

Your Turn 1 Use coordinate notation to write the rule that maps each preimage to its image Then identify the transformation Graph the Image P Q R to check your answer The coordinate rule is The transformation is Preimage P 4 2 Q 1 3 R 3 3 Image P 4 2 Q 1 3 R 3 3 P R 0

Your Turn Categorize if the transformation is a rigid motion or nonrigid motion The first three are done for you Rigid Motion the length shape and angle measure are preserved A B Nonrigid Motion the length shape or angle measure are NOT preserved C A D lifelong Geometry A LEARNING DID Credit 1 B E C F L4L Geometry A 2020 Page 133

6 Find m KLA if mLALM 88 and mzKLM 158 LKLA E K LCDJ M L A 7 Using the figure below LFDC 46 What is the measurement of b C b D 8 Find m CD if mLCDE 76 and m JDE 36 9 Find m RSW if mRST 150 and m WST 98 D C 46 Zb R ZRSW W E S T