2D Geometry Questions and Answers

7 6 A 10 9 8 7 6 5 4 3 fy 2 3 4 5 6 7 8 9 10 B 2 3 4 5 6 30 8 Position points A and B so they both lie on the graph of f g x

A 10 y 9 8 7 6 5 4 3 fr 3 J5 5 6 7 8 9 10 23 5 6 8 Position points A and B so they both lie on the graph of f g x

3 3 6 7 9 8 7 65 9 4 3 2 1 2 3 4 5 6 7 8 Y 1 2 3 4 4 2 5 3 6 Move the points so they do not coincide and both lie on the graph of fog f x x 1 g x x 2

8 The graph of a function h is shown Graph the inverse of h on the blank coordinate grid 10 5 0 5 0

Sore 23 Penalty back to zero Question Watch Video In the diagram below of triangle RST U is the midpoint of RT and V is the midpoint of ST If m TRS 33 5r and m LTUV 39 Se what is the measure of TUV Show Examples w UMAN S ay as and F PANG Toan ayam amare d Viruses found And

Draw AMGT Use the triangle to answer the questions below 1 What angle is included between GM MT and ZT 2 Which sides include 3 What angle is included between GT MG and

Given ARST with a point U inside such that ZRST ZRTS 42 and ZRSU ZSRU 18 Find ZUTS S U R

26 Given APOR ASTU m P 5x 30j mLQ 7x 35 mLT 4x 12y mzU 8y 2 Find MLP MLQ m R y MLS MLT mLU SHOW WORK You might want to draw a picture to help you get started but you don t have to

Find the point on the curve h x x2 8 that is closest to the point 18 8 Enter your answer as an order pair

The angle bisectors of AXYZ are XG YG and ZG They meet at a single point G In other words G is the incenter of AXYZ Suppose FG 17 YG 18 mz DXF 92 and m2 EYG 24 Find the following measures Note that the figure is not drawn to scale X D Y F E m LEYD DG 0 0 m LEZG 0 00 X UIU

Point Q is the midpoint of PR and PR 21 75 yards What is the length in yards of QR

The following graph shows a proportional relationship What is the constant of proportionality between y and in the graph 54 6 5 8 ON 1 29 3 4 12 5 Constant of proportionality 6 x

Part B Draw DE parallel to BC You can draw DE any length and place it anywhere on the coordinate plane but not on top of AABC Find and record the ratio n of the length of DE to the length of BC Then multiply the lengths of AB and CA by n and record the resulting lengths

In Exercises 3 6 use the diagram to write an example of the postulate 3 Two Point Postulate Postulate 2 1 4 Line Point Postulate Postulate 2 2 5 Plane Point Postulate Postulate 2 5 6 Plane Intersection Postulate Postulate 2 7 In Exercises 7 and 8 sketch a diagram of the description 7 RS bisecting KL at point R P B A 8 AB in plane U intersecting CD at point E

The angle of elevation to a nearby tree from a point on the ground is measured to be 74 How tall is the tree if the point on the ground is 54 Feet from the bottom of the tree Round your answer to the nearest tenth of a foot if necessary

Find the measure of the indicated angle Classify the triangle by angles and sides 1 MZA B 46 3 m20 N 7Y 4y 15 M 2 MZR 2x 2 T 4 mLE D 4x 1 3x 1 5x1 E

Sketch the graph of the function and check the graph with a graphing calculator Before doing so describe how the graph of the function can be obtained from the graph of a basic exponential function x 1 f x 5 Select the correct choice below and fill in the answer box to complete your choice OA Start with the graph of y Shift the graph 1 unit to the left OB X Start with the graph of y Shift the graph 1 unit down OC Start with the graph of y Shift the graph 1 unit up OD Start with the graph of y Shift the graph 1 unit to the right

2 Convert the following equation to its alternate form standard to slope intercept or vice versa 5 x 6 O 18x 30y 25 Ox y 5 O 18x 30y 25 O x y 1 3 Wilbur has sold 87 48 95 and 71 copiers in the last four months respectively How many copiers will he need to sell this month to maintain an average of at least 77 sales per month answer

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Find the value of the variable and all of the interior angle measures 1 2 W 468 5 vopos H 4 Find the value of the variable Find the measure of the exterior angle de variable F 3x 4 430 Solve for x and find any missing angle measures 03 12711x 74 12x 12x 50 0 37 46 17X XCHOGI OST 134 6 3 7x 4 6x 1 4x 1 126 F G H 5x 17 e Ova xat XP FF 5x 4 4x 9 X 9r 6

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WA00 Sketch the graph of the function and check the graph with a graphing calculator Before doing so describe how the graph of the function can be obtained from the graph of a basic exponential function X 4 f x 2 1 Describe how the graph of the function can be obtained from the graph of a basic exponential function Start with the graph of y Shift it 4 units and then shift it left up down 1 unit A 27

Lesson 2 1 Translations Learning Goal I can develop definitions of translations in terms of angles perpendicular lines parallel lines and line segments Standard G CO A 4 symbolically numerically and graphically A First draw a triangle on lined paper Label the vertices A B and C Then draw a line segment XY An example of what your drawing may look like is shown Using the same piece of tracing paper place A on A and draw a copy of AABC Label the corresponding vertices B and C An example of what your drawing may look like is shown EXPLORE Exploring Translations Read Explore in your textbook Lesson 2 1 and complete the following Show all your work A translation slides all points of a figure the same distance in the same direction You can use tracing paper to model translating a triangle ROIN BUse tracing paper to draw a copy of triangle ABC Then copy XY so that the point X is on top of point A Label the point made from Yas A X L4L Math Resources http Bit ly L4LMath Use a ruler to draw line segments from each vertex of the preimage to the corresponding vertex on the new image

For 12 19 determine the number of lines of symmetry for each shape 12 13 14 1 16 A 17 18 15 19

Angle Relationships Date me the relationship complementary supplementary vertical or adjacent 1 3 x Name the relationship alternate interior corresponding or alternate exterior 7 8 2 10

find the equation of the which points circumference passes through through the three A 1 3 B 2 4 and 6 2

draw the graphs of given 16y 18x 64y 71 0 2 a 9x 16y functions 2 b y 2x 6y 5 0

Learning Goal from Lesson 1 3 I can represent transformations visually e g by using manipulatives and or geometry software I can describe transformations as functions with inputs and outputs The points of the image are The resulting image is a 7 Use the rule x y 3x 2y to find the image for the preimage defined by the given points Then determine whether the transformation is a rigid motion or a nonrigid motion 2 points Preimage A 3 5 B 5 3 C 2 2 10 12 11 8 7 4 0 3 6 2 9 5 1 1 2 3 4 rigid 5 nonrigid 6 7 8 9 How I Did Circle one I got it motion Circle one 10 11 I m still learning it 13 14 12 15 16 17

B Which of the following transformations is needed to carry Figure ABCD onto its image A B C D 1 point 9 8 7 A 6 5 4 D 3 A x y x 5 y 4 B x y x 5 y 4 C x y x 4 y 5 D x y x 4 y 5 2 C 1 6 5 0 2 B 3 5 6 A D C B 6 1 2 7 8 9 10 11

Question Which of the following sets of numbers could represent the three sides of a triangle Answer Attempt out of 5 O 6 8 14 Watch Video O 13 20 34 Submit Answ

In AQRS RS 2 SQ 4 and QR 3 Which list has the angles of AQRS in order from largest smallest Answer Attempt 1 out of 5 O m R m Q m S O m Q m S m R O m Q m R m S Om S m R m Q O m S m Q m R O m R m S m Q Submit Answer

5 e Question Answer Attempt 1 out of 5 In APQR m P 101 and m Q 52 Which statement about the sides of APQR must be QRPQ RP RP PQ QR QR RP PQ O O RP QR PQ Watch Video PQ QR RP PQ RP QR Show Submit Answer

3 If EF is rotated about point C then which of the following segment pairs do not have to be of equal lengt 1 EF and EF 3 EC 2 CF CF and 4 FF and EE and EC

2 If ABC is mapped to A B C using a rigid body motion which of the following does not need to be true 1 AB is parallel to A B 2 m ABC mZA B C 3 BC B C 4 the midpoint of AB is mapped to the midpoint of A B 3 If EF is rotated about point C then which of the following segment pairs do not have to be of equal length 1 EF and E F 3 EC 2 CF and CF and E C 4 FF and EE

Find parametric equations and a parameter interval for the motion of a particle 25 four 2 starting at the point 5 0 and tracing the top half of the circle x y times Choose a correct possible parametrization below O A x 5 cost y 5 sint 0 t 4 OB x 5 cost y 5 sint 0 t 2 sin t 5 OC x y cos t 5 O D x 5 cost y 5 sint 0 t 2 0 t 4

Quadrilateral ABCD is mapped to quadrilateral ABCD Which of the following transformations would not result in the two quadrilaterals being congruent 1 a translation along side AB by a distance of twice AB 2 a dilation from point by a factor of one half 3 a rotation about point C by 90 counterclockwise 4 a reflection across side BC

Triangle DEF is formed by connecting the midpoints of the side of triangle ABC The lengths the sides of triangle ABC are shown Find the perimeter of triangle DEF Figures not necessar drawn to scale D

nt 12 Numeric Algebraic s Triangles ip EY Given Type Centroid nter Orthocenter Triangle Angles of the interior angles of triangle DEF are shown Find the measure of ZDIG Figures not necessarily drawn to scale F 47 D 71 H G 62 E

for Geometry ASSESSMENT Credit Checkpoint Complete the following problems Show all your work Learning Goal from Lesson 1 1 and 1 2 I can define the following terms precisely in terms of point line and distance along a line line segment angle and perpendicular lines a This shape will have 3 points A B and C Connect point B to point A using a line segment and connect point B to point C using a ray Using the figure you have drawn which of these are correctly shown AND named Select all that apply A line AB B AB OC angle BAC OD LCBA E BC How I Did Circle one 1 Draw a shape using the following directions Then check off which facts are true about the shape that you have drawn Lesson 1 1 1 2 point each lat I got it I m still learning it b This shape will have 4 points A B C and D Connect A B and C in a straight horizontal and continuous line Place D directly above B using a vertical line segment Using the figure you have drawn which of these are correctly shown AND named Select all that apply A AC B ABC C BD LAC D BD E BC

5 Use the given statement bank to fill in the following two column proof Two have been done for you Given mz1 m23 Prove m2PTR mSTQ Statements mz1 m23 m22 mc2 mz1 mz2 m43 m22 S mz1 m22 mzPTR m23 mz2 m STQ m2PTR mzSTQ A x 3 B x 7 C LM 14 D LM 28 E LN 26 F LN 54 6 If LM 3x 5 MN 4x and LN 11x 7 select ALL that are true L M T U N 7 Find the value of x Using that information find the measurement of UV 13 6 4x 29 Reasons 2r 18 Given Addition Property of Equality V 3 Statement Bank Addition Property of Equality Substitution Property Given na Reflexive Property Angle Addition Postulate

x 4 Solve for x given the two angles form a Linear Pair B 5 Segment RT 40 If RS 15 and ST 5x Find the value of x R 7 C 9x 10 40 6 Solve for x Using that value find the measurement of ZABE Hint All four corners of a perpendicular intersection is a right angle 6x 2 S 1x 20 E mLABE HOY Optional Complete problems 17 19 22 28 from your textbook on separate lined paper When you are finished check the odd problems for solutions at the back of the textbook

2 Use deductive reasoning to solve equation 3 4x 5 Use properties of Equality to justify each step 3 Write a justification for each step Choose from the following reasons Division Property of Equality Addition Property of Equality Segment Addition Postulate Simplify Substitution Property of Equality Subtraction Property of Equality H 7x 3 2x 6 73x 3 J HJ Hitl 7x 3 2x 6 3x 3 7x 3 5x 3 7x 5x 6 2x 6 x 3

Lesson 1 4 Homework HW 1 Find the value of angle b if the pair of angles are complementary Complete problems 1 6 below for independent practice When you are finished check the solutions with your teacher 63 O A 70 OB 140 C 35 OD 20 3 Segment RU is an angle bisector m QRU 70 What is m QRS Q S 2 Find the value of angle b given the pair of angles are supplementary L 650

pair Find mLABD 3 In the figure to the right the two angles form a linear pair Find mzDBC E OTEVE D B 135 C 5x 10 2x 5 F LL 9x 4 Ray HF is an angle bisector of ZEHG mzEHG 68 and mzFHG 9x 2 Find the value of x

A Angle bisector Las 26 5x 11 D Definition of Midpoint E Word Bank B Supplementary angles m 18 4m 2 E Complementary Angles 3r B 5r 6 C Segment Addition Postulate 9000 D

1 Use coordinate notation to write the rule that maps each preimage to its image Then identify the transformation Graph the Image R S T to check your answer The coordinate rule is The transformation is lifelong Geometry A Preimage R 4 3 S 1 3 T 4 1 Credit 1 Image R 4 3 S 1 3 T 4 1 R T 5 L4L Geometry A 2020 O X Page 134

I can prove the following theorems angles 9 If AT 2x 1 TL 15 and AL 7x 1 select ALL that are true 1 point A x 5 B x 3 C AT 7 D AT 11 E AL 35 F AL 22 10 If line segment SU is an angle bisector of TSV mZTSV 62 and mzVSU 5x 1 find the value of x 1 point 11 Find the value of q given the angles are a linear pair Using that information find the measurement of ZDBC 1 point I got D 7q 46 3q 6 B Checkpoint Score Total

The ray B y BD is the angle bisector of ZABC and mLABC 110 Find mzABD Lesson 1 2 1 point O B 5 If ray RS bisects OQ name two angles that are complementary Name two angles that are supplementary Lesson 1 2 1 point S D R C Q 4 Ray RU bisects ZQRS If mZSRU 50 and m2QRU x 10 Find the value of x Find mzQRS Lesson 1 2 1 point Q F t 70 6 m2HGF 145 mLEGF 110 Find the measure of ZHGE Lesson 1 2 1 point G H E S

2 Find the midpoint and length distance between each pair of points Lesson 1 1 2 point each Midpoint Formula x x2 Y y2 Distance Formula x x y y 2 a 4 7 and 2 9 Midpoint b 5 5 and 1 3 Midpoint Length Length is Length Length is