Geometry Questions

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

WS Mix with Algebra Systems of Equations and Quadratics 1 Triangle MNP and OMNare equilateral triangles What method can be used to verify the triangles are congruent Find the value of x and y 3X 12 X 4 M 3x 12 3 In triangle ABC AD is the perpendicular bisector of BC AB 25 AC 3x 5 and mLADC y 35 What method can be used to verify the triangles are congruent Find the value of x and y 4 What method can be used to verify the triangles are congruent If RQ 5x 2 RS 3x 8 and PQ 2x 4 find the value of xand all sides 3y 6 O x 4 2 Triangle ABC and DEFhave the following properties ABDE BC EF and LB LE If AB 27 BC 4 DE 7x 3y and EF 2x y What method can be used to verify the triangles are congruent Find the value of xand y N A B D C

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

Find the length of GH F I GH 5 8 2 G J H Write your answer as a whole number or a decima

If GH GJ m GIH 6b and mZGIJ b 60 what is mZGIJ G H J I

If JK 9w 67 and GI 2w 12 what is the value of w G H I

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

of point line and distance along a line line lowing terms precisely in terms segment angle and perpendicular lines P 3x 5 Lesson 1 2 Checkpoint Once you have completed the above problems and checked your solutions complete the Lesson below Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 OS bisects PQR What is mzPQR Hint Solve for x and plug the value back in Don t forget to add the final two angles together 2 25 Starting S Getting there R Got it We in

10 MA bisects segment CB at midpoint M Based on the definition of angle bisector and midpoint find the value of x and the following measures MB CM CB O 0 B

HW 1 Which of the following is NOT a property of perpendicular lines A They intersect at one point B They intersect to form a Right Angle C The intersection can form 90 angles OD They intersect to form acute angles A 4 Which of the following is NOT properly named based on the figure below 4 C Complete problems 1 10 for independent practice When you are finished check the solutions with your teacher B A ray CA B LACB C ray AB OD ZBCA 3 Which of the following is NOT a type of bisector A Dimensional Bisector B Segment Bisector C Perpendicular Bisector D Angle bisector 5 Which of the following best classifies the angle measurement of ZLMN 0000 L M N A Acute Angle B Right Angle C Obtuse Angle D Straight Angle R

MP bisects segment LN at midpoint M Based on the definition of angle bisector and midpoint find the measures of m 1 segment LM and MN m21 LM MN 1 M LN 30

EXPLAIN 3A Constructing an Angle Bisector Read Explain 3A and complete Your Turn 1 2 adapted from Lesson 1 2 An angle bisector is a ray that divides an angle into two angles that both have the same measure In the figure BD bisects LABC so m ABD m CBD The arcs in the figure show equal angle measures Example 1 BD bisects LABC What is m ABC Information Solve Ego mzDBC mzABD 65 mzABC mLABD mzDBC m ABC 65 65 mzABC 130 8 Determine the value of x 26 5x 11 26 5x 11 Definition of an angle bisector 15 5x Subtract 11 on both sides Divide by 5 on both sides 3 x Your Turn If m FCD x 48 mzBCF x 17 and m BCD 95 then find the value of x B C F D

1 Draw the segment PQ with endpoints P 2 1 and Q 2 4 on the coordinate plane 2 Find the midpoint of PQ 3 Find the length of PQ Learning Goal 4 2 ty 4 2 0 2 4 2

Determine if the angle pairs are complementary supplementary or neither given m PRO 99 mzPRQ 81 mzPRS 9 and m2ORS 90 1 ZPRQ and ZPRO are 2 LORS and LPRS are 3 20RS and LSRQ are 4 ZPRQ and LPRS are ST P R

Name 22 in many different ways as possible 22 8 M 3 2 E D Without seeing a figure give another name for ZMKG

HW 1 Which of the following is the correct way to name a line segment A AB B CD OCEF OD DC plete problems 1 10 for independent practice When you are finished check the solutions with your teacher 3 All points between and including endpoints describes which of the following terms A angle OB line OC line segment Dray 5 Which of the following is the midpoint formula A a b c B 1 2 X C x y z OD 221 22 21 2 What does the symbol QR represent A line segment QR OB angle QR C ray QR OD line QR 4 If BD is bisected by point C then BC CD BD 0000 A Segment Addition Postulate B Definition of a Midpoint C Addition Property of Equality D Definition of an Angle Bisector 6 Which of the following is the distance formula A x x y y B x y x y C x y x y D x x y y

Calculate the length between the following points using the distance formula 1 6 and 7 14 10 Calculate the length between the following points using the distance formula 3 2 and 9 3

7 What is the midpoint for a segment with the following endpoints 4 5 and 10 3 8 What is the midpoint for a segment with the following endpoints 2 3 and 11 20 2

7 e kolu olan bir merdiven bir ucu duvar zerine gelecek bi imde zemin zerinde konumland nda olu an a l leri ekilde veriliyor Duvar Zemin 55 A 80 B B 85 X E 65 A E ve B do rusal oldu una g re m AEA x ka derecedir C 90 A B D 95 E 100 6 A 7 B

Determine the value of x for which r s Then find m21 and m22 m 1 30 6x m2 40 26x The value of x for which r II s is Type an integer or a decimal m21 Type an integer or a decimal m22 Type an integer or a decimal S 2

Use the graphs of f and r to describe the transformation from the graph of f to the graph of r f x 3r 5 The graph of r is a of the graph of flby a factor of

How many significant figures should be recorded for the answer to the multiplication problem below 24 32 x 0 010 significant figures

4 J I K A reflection across x 1 B reflection across y 2 C reflection across the y axis D reflection across x 2 x

ANALYZING RELATIONSHIPS In the diagram JKLM EFGH Find the values of x y and z H3G 21 11 E 8 F 20 65 K 30 M L

The polygons are similar The area of one polygon is given Find the area of the other polygon 4 cm A 10 cm Area cm 12 cm

The graph of f x is shown below Find the graph of f x N 10 4 20 2 1 5 1 2 3 4 5 6

50 Think back to August 6 1945 The United States has just dropped an atomic weapon on the city of Hiroshima killing tens of thousands of Japanese and devastating the infrastructure A Keynesian at that time might conclude that there is a silver lining in the destruction as economic prosperity will result Evaluate the logic of this claim in a few sentences

If JM 5x 8 and LM 2x 6 which expression represents JL J O 3x 2 O 3x 14 07x 2 O 7x 14 K M

Use suitable labelled line diagrams to show how the following tools are used to check the squareness of a simple rectagular building Builder s square

A DA C120 6 m B B

Identify the type of transformation What is the image of segment FG

b Jae ti Hort u

as o tas tion b u

If TU p 4 and SV p 44 what is the value of p W T S HH V

XZ is a midsegment of AVWY If VW p and XZ p 25 what is the value of p Y V N X W