Lesson 4.1 Triangle Sum Conjecture

Similar documents
Lesson 4.1 Triangle Sum Conjecture

Lesson 4.1 Triangle Sum Conjecture

Lesson 4.1 Triangle Sum Conjecture

Lesson 5.1 Polygon Sum Conjecture

Use the diagram to identify each angle pair as a linear pair, vertical angles, or neither.

Pre-AP Geometry Worksheet 5.2: Similar Right Triangles

2) Three noncollinear points in Plane M. [A] A, D, E [B] A, B, E [C] A, B, D [D] A, E, H [E] A, H, M [F] H, A, B

MEP Practice Book ES3. 1. Calculate the size of the angles marked with a letter in each diagram. None to scale

Answers for Lesson 3-1, pp Exercises

9.5 Start Thinking. 9.5 Warm Up. 9.5 Cumulative Review Warm Up

R(3, 8) P( 3, 0) Q( 2, 2) S(5, 3) Q(2, 32) P(0, 8) Higher Mathematics Objective Test Practice Book. 1 The diagram shows a sketch of part of

12.4 Similarity in Right Triangles

Geometry AP Book 8, Part 2: Unit 3

Essential Question What conjectures can you make about perpendicular lines?

Calculus AB Section I Part A A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION

Triangles The following examples explore aspects of triangles:

Mathematics 10 Page 1 of 5 Properties of Triangle s and Quadrilaterals. Isosceles Triangle. - 2 sides and 2 corresponding.

T 1 T 2 T 3 T 4 They may be illustrated by triangular patterns of numbers (hence their name) as shown:

THE KENNESAW STATE UNIVERSITY HIGH SCHOOL MATHEMATICS COMPETITION PART I MULTIPLE CHOICE NO CALCULATORS 90 MINUTES

Answers to Exercises. c 2 2ab b 2 2ab a 2 c 2 a 2 b 2

3 Angle Geometry. 3.1 Measuring Angles. 1. Using a protractor, measure the marked angles.

8.6 The Hyperbola. and F 2. is a constant. P F 2. P =k The two fixed points, F 1. , are called the foci of the hyperbola. The line segments F 1

Prove Lines are Parallel. p Use angle relationships to prove that lines are parallel. VOCABULARY. Paragraph proof

GEOMETRY OF THE CIRCLE TANGENTS & SECANTS

Parallel Projection Theorem (Midpoint Connector Theorem):

Unit 5 Review. For each problem (1-4) a and b are segment lengths; x and y are angle measures.

Precalculus Due Tuesday/Wednesday, Sept. 12/13th Mr. Zawolo with questions.

Similarity and Congruence

KEY CONCEPTS. satisfies the differential equation da. = 0. Note : If F (x) is any integral of f (x) then, x a

List all of the possible rational roots of each equation. Then find all solutions (both real and imaginary) of the equation. 1.

A LEVEL TOPIC REVIEW. factor and remainder theorems

13.3 CLASSICAL STRAIGHTEDGE AND COMPASS CONSTRUCTIONS

S56 (5.3) Vectors.notebook January 29, 2016

2 Calculate the size of each angle marked by a letter in these triangles.

Believethatyoucandoitandyouar. Mathematics. ngascannotdoonlynotyetbelieve thatyoucandoitandyouarehalfw. Algebra

REVIEW SHEET FOR PRE-CALCULUS MIDTERM

Nat 5 USAP 3(b) This booklet contains : Questions on Topics covered in RHS USAP 3(b) Exam Type Questions Answers. Sourced from PEGASYS

GEOMETRICAL PROPERTIES OF ANGLES AND CIRCLES, ANGLES PROPERTIES OF TRIANGLES, QUADRILATERALS AND POLYGONS:

ES.182A Topic 32 Notes Jeremy Orloff

1 ELEMENTARY ALGEBRA and GEOMETRY READINESS DIAGNOSTIC TEST PRACTICE

Geometry Student Text and Homework Helper

Faith Scholarship Service Friendship

8. Complex Numbers. We can combine the real numbers with this new imaginary number to form the complex numbers.

MTH 4-16a Trigonometry

Alg 3 Ch 7.2, 8 1. C 2) If A = 30, and C = 45, a = 1 find b and c A

DA 3: The Mean Value Theorem

Chapter 5 Test, Form 2A

from X to GH. 17. What is the distance from M(9, 4) to N( 1, 2)? of A?geometry Review #1 for MP3 Exam A If MX 21.6, find LZ and MW.

m m m m m m m m P m P m ( ) m m P( ) ( ). The o-ordinte of the point P( ) dividing the line segment joining the two points ( ) nd ( ) eternll in the r

Name Date. In Exercises 1 6, tell whether x and y show direct variation, inverse variation, or neither.

Lesson 8.1 Graphing Parametric Equations

Plotting Ordered Pairs Using Integers

STRAND J: TRANSFORMATIONS, VECTORS and MATRICES

Lesson 2.1 Inductive Reasoning

Geometry of the Circle - Chords and Angles. Geometry of the Circle. Chord and Angles. Curriculum Ready ACMMG: 272.

MCR 3U Exam Review. 1. Determine which of the following equations represent functions. Explain. Include a graph. 2. y x

10.2 The Ellipse and the Hyperbola

GM1 Consolidation Worksheet

A B= ( ) because from A to B is 3 right, 2 down.

1. Extend QR downwards to meet the x-axis at U(6, 0). y

Mathematics Extension 1

UNCORRECTED. 9Geometry in the plane and proof

Linear Inequalities: Each of the following carries five marks each: 1. Solve the system of equations graphically.

FUNCTIONS: Grade 11. or y = ax 2 +bx + c or y = a(x- x1)(x- x2) a y

Mathematics. toughest areas of the 2017 exam papers. Edexcel GCSE (9-1) Higher. guided exam support on the top 10 toughest

Problem Set 9. Figure 1: Diagram. This picture is a rough sketch of the 4 parabolas that give us the area that we need to find. The equations are:

Form 5 HKCEE 1990 Mathematics II (a 2n ) 3 = A. f(1) B. f(n) A. a 6n B. a 8n C. D. E. 2 D. 1 E. n. 1 in. If 2 = 10 p, 3 = 10 q, express log 6

CONIC SECTIONS. Chapter 11

Chapter 1 Cumulative Review

APPM 1360 Exam 2 Spring 2016

Calculus Module C21. Areas by Integration. Copyright This publication The Northern Alberta Institute of Technology All Rights Reserved.

Higher Maths. Self Check Booklet. visit for a wealth of free online maths resources at all levels from S1 to S6

Log1 Contest Round 3 Theta Individual. 4 points each 1 What is the sum of the first 5 Fibonacci numbers if the first two are 1, 1?

Lesson 2.1 Inductive Reasoning

4. Statements Reasons

TO: Next Year s AP Calculus Students

( β ) touches the x-axis if = 1

Advanced Algebra & Trigonometry Midterm Review Packet

First Semester Review Calculus BC

C Precalculus Review. C.1 Real Numbers and the Real Number Line. Real Numbers and the Real Number Line

Alg. Sheet (1) Department : Math Form : 3 rd prep. Sheet

Date Lesson Text TOPIC Homework. Solving for Obtuse Angles QUIZ ( ) More Trig Word Problems QUIZ ( )

Quotient Rule: am a n = am n (a 0) Negative Exponents: a n = 1 (a 0) an Power Rules: (a m ) n = a m n (ab) m = a m b m

Math Sequences and Series RETest Worksheet. Short Answer

Objective: Use the Pythagorean Theorem and its converse to solve right triangle problems. CA Geometry Standard: 12, 14, 15

English Metric Conversions

The Trapezoidal Rule

m A 1 1 A ! and AC 6

4.1 One-to-One Functions; Inverse Functions. EX) Find the inverse of the following functions. State if the inverse also forms a function or not.

3.1 Review of Sine, Cosine and Tangent for Right Angles

Andrew Ryba Math Intel Research Final Paper 6/7/09 (revision 6/17/09)

10 If 3, a, b, c, 23 are in A.S., then a + b + c = 15 Find the perimeter of the sector in the figure. A. 1:3. A. 2.25cm B. 3cm

8Similarity UNCORRECTED PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8.

MEP Practice Book ES19

EC and AB because AIA are congruent Substituting into the first equation above

Find the value of x. Give answers as simplified radicals.

Section 1.3 Triangles

Maintaining Mathematical Proficiency

THE PYTHAGOREAN THEOREM

, MATHS H.O.D.: SUHAG R.KARIYA, BHOPAL, CONIC SECTION PART 8 OF

Transcription:

Lesson.1 ringle um onjecture Nme eriod te n ercises 1 9, determine the ngle mesures. 1. p, q., 3., 31 8 p 98 q 8 53 17 79 3 50. r, s, 5.,. t t 85 s 100 r 30 100 7 31 7. s 8. m 9. m s 7 35 m c c 10. Find the mesure of. 11. Find the sum of the mesures of the mrked ngles. 1. Use the digrm to eplin wh 13. Use the digrm to eplin wh nd re complementr. m m m m. iscovering Geometr rctice our kills H 9 015 Kendll Hunt ulishing

Lesson. roperties of sosceles ringles Nme eriod te n ercises 1 3, find the ngle mesures. 1. m. m G 3. 110 58 N G n ercises, find the mesures.. m, perimeter 5. he perimeter of L. he perimeter of is of is 53 m. L, 3 cm. m, m 13 cm 7 cm 10 31 cm8 10 m 39 L 30 13 m 7.. Nme the ngle(s) congruent to.. Nme the ngle(s) congruent to. c. Wht cn ou conclude out nd? Wh? 8., 9. nd. 10. Use the digrm to eplin f m 10, wht is wh is isosceles. m? 79 70 55 30 H iscovering Geometr rctice our kills 015 Kendll Hunt ulishing

oordinte Geometr oint of oncurrenc: entroid Nme eriod te For ercises 1 3, find the midpoint of ech segment. 1.. 3. (, ) ( 3, ) (3, 1) (, ) (1, 5) F (, ) For eercises, grph the medins of the tringle. dentif the centroid.. 5. 8. 5 5 5 L N For ercises 7 nd 8, use the tringle from ercise. 7. Find the eqution of the line tht contins the medin from to. 8. Find the eqution of the line tht contins the medin from to. For ercises 9 1, find the coordintes of the centroid for ech tringle 9. 10. 5 11. 1. L N 8 iscovering Geometr rctice our kills H 31 015 Kendll Hunt ulishing

Lesson.3 ringle nequlities Nme eriod te n ercises 1 nd, determine whether it is possile to drw tringle with sides of the given mesures. f it is possile, write es. f it is not possile, write no nd mke sketch demonstrting wh it is not possile. 1. 1 cm, 30 cm, 5 cm. 9 km, 17 km, 8 km 3. f 17 nd 3 re the lengths of two sides of tringle, wht is the rnge of possile vlues for the length of the third side? n ercises, rrnge the unknown mesures in order from gretest to lest.. 5. c. 3 13 18 c 1 0 71 8 c 0 d 7. 8. 9. Wht s wrong with this picture? 1 158 10 10 10. plin wh is isosceles. n ercises 11 nd 1, use compss nd strightedge to construct tringle with the given sides. f it is not possile, eplin wh not. 11. 1. 3 H iscovering Geometr rctice our kills 015 Kendll Hunt ulishing

Lesson. re here ongruence hortcuts? Nme eriod te n ercises 1 3, nme the conjecture tht leds to ech congruence. 1.. JN 3. isects,, nd n ercises 9, nme tringle congruent to the given tringle nd stte the congruence conjecture. f ou cnnot show n tringles to e congruent from the informtion given, write cnnot e determined nd redrw the tringles so tht the re clerl not congruent.. is the midpoint of 5. K is kite with K.. nd. K 8 9 9 8 J N K 7. N 8. 9. N U G 10 8 8 10 n ercises 10 1, use compss nd strightedge or ptt pper nd strightedge to construct tringle with the given prts. hen, if possile, construct different (noncongruent) tringle with the sme prts. f it is not possile, eplin wh not. 10. 11. 1. U U iscovering Geometr rctice our kills H 33 015 Kendll Hunt ulishing

Lesson.5 re here ther ongruence hortcuts? Nme eriod te n ercises 1, nme tringle congruent to the given tringle nd stte the congruence conjecture. f ou cnnot show n tringles to e congruent from the informtion given, write cnnot e determined nd eplin wh. 1.. VW 3. V W. is the ngle isector 5. N. FGH is prllelogrm. of. G. N L F K G L H 7. he perimeter of is 350 cm. 8. he perimeter of UV is 95 cm. s L? plin. s UV WV? plin. L 55 10 U 70 15 5 V 15 0 W n ercises 9 nd 10, construct tringle with the given prts. hen, if possile, construct different (noncongruent) tringle with the sme prts. f it is not possile, eplin wh not. 9. 10. 3 H iscovering Geometr rctice our kills 015 Kendll Hunt ulishing

Lesson. orresponding rts of ongruent ringles Nme eriod te 1. Give the shorthnd nme for ech of the four tringle congruence conjectures. n ercises 5, use the figure t right to eplin wh ech congruence is true. W is prllelogrm.. W 3. W W. W 5. W For ercises nd 7, mrk the figures with the given informtion. o demonstrte whether the segments or the ngles indicted re congruent, determine tht two tringles re congruent. hen stte which conjecture proves them congruent.. is the midpoint of W nd 7. is isosceles nd is the isector. s W? Wh? of the verte ngle. s? Wh? W n ercises 8 nd 9, use the figure t right to write prgrph proof for ech sttement. 8. F 9. F F 10. is n isosceles trpezoid with nd. Write prgrph proof eplining wh. iscovering Geometr rctice our kills H 35 015 Kendll Hunt ulishing

Lesson.7 Flowchrt hinking Nme eriod te omplete the flowchrt for ech proof. 1. Given: nd how: Flowchrt roof Given. Given: Kite K with K K how: K isects K nd K Flowchrt roof K K K K K is kite K efinition of isect 3. Given: is prllelogrm how: Flowchrt roof is prllelogrm efinition of me segment 3 H iscovering Geometr rctice our kills 015 Kendll Hunt ulishing

Lesson.8 roving pecil ringle onjectures Nme eriod te n ercises 1 3, use the figure t right. 1. is medin, perimeter 0, nd.. is n ngle isector, nd m 5. m 3. is n ltitude, perimeter, m 38, nd 8. m,. U is equilterl. 5. NG is equingulr m nd perimeter NG 51. N. is equilterl, is isosceles with se, perimeter, nd perimeter 8. erimeter 7. omplete flowchrt proof for this conjecture: n n isosceles tringle, the ltitude from the verte ngle is the medin to the se. Given: sosceles with nd ltitude how: is medin Flowchrt roof is n ltitude nd re right ngles efinition of ltitude Given 8. Write flowchrt proof for this conjecture: n n isosceles tringle, the medin to the se is lso the ngle isector of the verte ngle. Given: sosceles with nd medin how: isects iscovering Geometr rctice our kills H 37 015 Kendll Hunt ulishing