Geometry Questions

A surfer is riding a 7 foot wave The angle of depression from the surfer to the shoreline is 10 What is the distance from the surfer to the shoreline

A cell phone tower is anchored by two cables on each side for support The cables stretch from the top of the tower to the ground with each being equidistant from the base of the tower The angle of depression from the top of the tower to the point in which the cable reaches the ground is 23 If the tower is 140 feet tall find the ground distance between the cables

12 A fire hydrant sits 72 feet from the base of a 125 foot tall building the fire hydrant to the top of the building

10 Jada is standing 10 feet from the base of tree and spots a nest sitting on a branch The angle of elevation from the ground where she is standing to the nest is 55 Find the height of the nest

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4 Name the figure below and solve for x 5x 139 92 wn angle measures for the quadrilateral in the diagram 9 1 71 3x 1260 2 180 7 1 2 5 n The polygon is a pentagon 2x 5 Name the figure below and solve for x 5x x 8 n Ya 75 5 8 25 Explain the Error Find and explain what this student did incorrectly when solving the following problem What type of polygon would have an interior angle sum of 1260

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

1 Cross two ducks with a match Answer L 180 110 2 Cross a stick of dynamite with a lemon pie Answer T 113 68 63 34 34 54 38 54 67 99 57 90 36 59 67 Find the angle measures indicated Look for each answer in the code Each time the answer appears write the letter of the exercise above it 40 37 57 99 67 104 76 59 113 42 53 67 99 18 A mzPQR E mzPQT m28 57 F mZMNL K m2M 83 B 67 R N C S 37 29 K G m J 115 B MIDDLE SCHOOL MATH WITH PIZZAZZI BOOK D Creative Publications 56 A N mZDAB OmZDAC 41 D QmZEFD B MZE D 35 D E F U S mZWOX X 72 104 59 79 mZXZY U m2Y 180 79 42 B A W 27 X 138 180 Systolet Z M MZAOB R mZBOC O 0 54 D TOPIC 3 k Review Related Ang

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

In ANOP T is the centroid If TQ 6 find PT O Q N R T S P

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

Answer Attempt 1 out of 5 Equilateral O Isosceles Acute Scalene Acute D Isosceles Right 43 4 6 7 85 102 C 5 49 35 B Isosceles Obtuse O Scalene Obtuse O Scalene Right S

5 After performing the translation described below what will be the coordinate of point M translation x y x 7 y 1 Ay Moy thew enoudes on wollo sit30 das S ANDRETT 6 After performing the translation described below what will be the coordinate of point R translation x y x 5 y 1 Ay Che R

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

In the diagram below of triangle UVW X is the midpoint of UW and Y is the midpoint of VW If XY 6x 61 and UV 3x 17 what is the measure of UV U X W Y Show Examples V

X 2 OA HAMMAD SAMAS wwwwww OB 4 OC QO

The equation gives parame equations and parameter intervals for the motion of a particle in the xy plane Identify the particle s path by finding a Cartesian equation for it Graph the Cartesian equation Indicate the portion of the graph traced by the particle and the direction of motion x 4t 3 y 16t t y x 3 Graph the Cartesian equation below Indicate the direction of motion as t increases Choose the correct graph below OA OB O C 10 40 10 TIH I Ay Indicate the portion of the graph traced by the particle Select the correct choice below and if necessary fill in the answer box to complete your choice OA The portion of the graph where t is less than B None of the graph C The entire graph OD The portion of the graph where t is greater than

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

or geometry software I can describe transformations as tions visually eg by using manipulatives functions with inputs and outputs Lesson Reflection Circle one Starting Getting there Got it Lesson 1 3 Checkpointsu bas svarbai galiolges 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 Draw the image of the figure under the given transformation Then describe the transformation as a rigid motion or not a rigid motion Justify your answer y 0 5x y 4 2 Match each transformation with the correct description A x y 3x y B x y x 3 y C x y x 3y D x y x y 3 E x y 3x 3y S S dilation with scale factor 3 translation 3 units up translation 3 units right horizontal stretch by a factor of 3 vertical stretch by a factor of 3

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

Home W Assignment 12 Midsegment Numeric Midsegment Algebraic es of Isosceles Triangles de Relationship ngle Inequality Triangles of a Given Type Triangle Lines Centroid enter Incenter Orthocenter and Exterior Triangle Angles Triangle LMN is formed by connecting the midpoints of the side of triangle IJK The lengths the sides of triangle LMN are shown What is the length of IJ Figures not necessarily drawn scale Answer Attempt 1 out of 5 N 2 L 2 2 K M J G

5 After performing the translation described below what will be the coordinate of point M translation x y x 7 y 1 11 M 9 5 8 8 5 M 6 After performing the translation described below what will be the coordinate of point R D Whe For 7 10 Name the type of transformation shown by the given rules The names you can choose from are Reflection Translation Rotation Dilation 7 x y x y 8 6 2 12 4 translation x y x 5 y 1 A R Match each transformation with the correct description A x y x y B x y x y C x y x y 43 10 x y x 9 y 2 7 reflection across the y axis rotation of 180 about the origin reflection across the x axis Optional Complete problems 1 2 4 8 15 from your textbook on separate lined paper

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

EXPLAIN 1 Introducing Proofs Read Explain 1 and complete Your Turn 1 3 adapted from Lesson 1 4 A conjecture is a statement that is believed to be true You can use inductive or deductive reasoning to show or prove that a conjecture is true Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true Deductive reasoning is the process of using logic to draw conclusions A conditional statement is a statement that can be written in the form If p then q where p is the hypothesis and q is the conclusion For example in the conditional statement If 3x 5 13 then x 6 the hypothesis is 3x5 13 and the conclusion is x 6 Most of the Properties of Equality can be written as conditional statements You can use these properties to solve an equation like 3x 5 13 to prove that x 6 Properties of Equality Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality Reflexive Property of Equality Symmetric Property of Equality Transitive Property of Equality Substitution Property of Equality Example Use deductive reasoning to solve the equation Use properties of Equality to justify each step 1 14 3x 4 18 3x If ab then a c b c If ab then a c b c If ab then ac bc If a b and c 0 then ama If a b then b a If a band b c then a c If ab then b can be substituted for a in any expression 6 x x 6 Addition Property of Equality Division Property of Equality Symmetric Property of Equality Your Turn 1 Identify the Property of Equality that is used in each statement If x 2 then 2x 4 5 3a therefore 3a 5 If T 4 then 5T 7 equals 27 If 9 4x and 4x m then 9 m

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

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

1 Assuming counterclockwise rotations where would the following land Aelavkea 1 216 degree rotation of D about F 0 432 degree rotation of EA about F 144 degree rotation of ZDFC about F Be E

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

What type of reasoning is used in the story below Is it poor or strong logic Why Dan noticed that each of the four times he ate a hamburger and shake at the Fast Food Emporium he got a poor grade on a Spanish test that day He conjectures that he should eat only Mexican food on the day of a Spanish test