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Transcript

Unit 1 PACKET (1.2-1.8 (Omit 1.6), 2.6, 3.1-3.4) DATE LESSON ESSENTIA L QUESTIO N I WILL…. Assignments (Day 1) BW: Vocab and 8/22 Due: 8/25 or 8/26 Lesson 1.2: Points, Lines, and Planes Pages 11-19 What are the accepted facts and basic terms and definitions of geometry? Postulate Chart CW/HW: Use the textbook to Lesson 1.2 define, name, and draw Notes the accepted facts and basic terms of Pg.16 #1-3 geometry. WB 9 EXIT: 1. Pg.16 #5 and #7 BW: 8/23 Due: 8/25 or 8/26 Lesson 1.3: Measuring Segments Pages 20-26 How can you use number operations to find and compare lengths of segments? Use number operations to find and compare lengths of segments. #1 CW/HW: Vocab Lesson 1.3 Notes Pg.23 #1-6 WB 13 EXIT: Page 24 #7 BW: 8/24 Lesson 1.4: Measuring Angles Due: 8/25 or 8/26 Pages 27-33 How can you use number operations to find and compare the measure of angles? Use number operations to find and compare the measure of angles. Key concepts /Postulate 1.8 CW/HW: Lesson 1.4 Notes Pg.31 #1-4 WB17 EXIT: Pg.31 #5 BW: 8/25 Or 8/26 Due: 8/25 or 8/26 Lesson 1.5: Exploring Angle Pairs Pages 34-40 How can special angle pairs help you identify geometric relationships? Use special angle pairs to find angle measures. #2 CW/HW: KC/V/P1.9 Lesson 1.5 Notes Pg.37 #1-5 WB 19-20 #4-7, 9, 17, 20 WB 21 EXIT: pg.37 #6 Assignments (Day 2) 8/29 8/30 Due: 9/1 Or 9/2 8/31 9/1(2) Due: 9/1 Or 9/2 9/1(2) Due: 9/6 9/7 9/8(9) Due: 9/8(9) Lesson 1.7: Midpoint and Distance in the Coordinate Plane How can you find the midpoint and length of any segment in a coordinate plane? Use the midpoint and distance formulas to find the length of segments in the coordinate plane. Pages 50-56 Lesson 1.8: Perimeter, Circumferen ce, and Area Pages 59-67 How do you find the perimeter and area of geometric figures? Use the formulas for perimeter and area measure geometric figures. BW: #3 CW/HW: KC Lesson Notes 1.7 Pg.53 #1-4 EXIT: Pg.53 #5 Pg.55 #5253 BW: #4 CW/HW: KC/V/P1.10 Lesson Notes 1.8 Pg.64 #1-3 EXIT: Pg.64 #6 Due: 9/15 (16) 9/14 9/15(6) Due: 9/15 (16) EXIT: Pg.55 #56 BW: Pg.65 #27, 32 CW/HW: WB 31-32 (even) WB 33 EXIT: Pg.66 #48 BW: Pg.70 #1-4 CW/HW: Pg.71-74 #7-41 (odd) Review/Ass ess EXIT: Pg.75 #2023 Lesson 2.6: Proving Angles Congruent How can you prove theorems as reasons in a proof? BW: Theorems CW/HW: Prove and apply Lesson Notes 12.6 theorems about angles. Pg.124 #1-3, 5 EXIT: 9/12 9/13 BW: Pg.54 #31,32 CW/HW: WB 27-28 (even) WB 29 What special Lesson 3.1: angle pairs Lines and are formed Angles by transversals ? Lesson 3.2: Properties of Parallel Lines What are the properties of parallel lines? BW: #5 CW/HW: WB 55-57 EXIT: Pg.125 #19 Pg.124 #4 BW: BW: KC #6 CW/HW: Identify the special CW/HW: Lesson 3.1 angle pairs formed by WB 59-61 Notes EXIT: a transversal. Pg.143 #1-9 Pg.144 EXIT: #24 Pg.143 #10 BW: Identify and justify #7 congruent and CW/HW: supplementary angles KC using my knowledge Lesson 3.2 of the properties of Notes parallel lines. Pg.152 #1-5 BW: Pg.153 #15, 16 CW/HW: WB 63-65 EXIT: EXIT: Pg.152 #6 9/15 (16) BW: Pg.132 #38 CW/HW: Pg.134 #3237 Pg.208 #1624 EXIT: Pg.211 #17, 18 Review/Ass essment 9/19 BELL WORK #1. #2. Pg.154 #22 Assessment Packet 1 Turn in #3. #4. #5. #6. #7. BELL WORK 1.2 Points, Lines, and Planes Vocabulary Term Description A _______________ indicates a location and has no size. How to Name It You can represent a point by a _________ and name it with a _________________ ___________________. A ________ is represented by a straight You can name a line by any _______ path that extends in two ____________ _____________ on the line, or by a single directions without end and has no ____________ ______ letter. ____________. A line contains infinitely many ___________. A ___________ is represented by a ________ surface that extends without You can name a plane by a _______ and has no _____________ letter or by any three ___________________. __________ in the plane. A plane contains infinitely many ____________. What are the names of three collinear Points that lie on the same _________ are points? called _______________ ____________. Points ____, _____, and ____ are collinear. Points and lines that lie in the What are the names of four coplanar _____________ plane are points? ________________. _____ the points of a Points _____, ____, _____, and ____ are _______ are coplanar. coplanar. _________ is the set of all ____________ in three dimensions. A ________________ is part of a line that You can name a segment by its ________ consists of two _____________ and all __________________. points _______________ them. A ______ is part of a line that consists of the endpoint. You can name a ray by its _____________ and another ___________ on the ray. The ____________ of the points indicates the ray’s _________________. ____________ __________ are ________ You can name opposite rays by their rays that share the ________ endpoint and __________ endpoint and _______ other form a _________. ____________ on each ray. one ________________ and all the ______________ of the line on one side of Diagram A __________________ OR (Please see the table of Postulates _________________ is an accepted 1-1, 1-2, 1-3, and 1-4 below.) statement or fact. Postulates, like ________________ terms, are basic building blocks of the __________________ system of geometry. You will use ________________ _____________________ to prove general concepts. When you have two or more geometric figures, their __________________ is the set of points the ______________ have in _______________. Postulate Name Postulate 1-1 Postulate 1-2 Postulate 1-3 Postulate 1-4 Description Through any two points there is exactly one __________. If two distinct lines intersect, then they intersect in exactly one _______. If two distinct planes ____________, then they ______________ in exactly one line. Through any three noncollinear points there is exactly one _____________. Diagram 1.3 Measuring Segments Vocab: The real number that _____________________ to a point is called the ____________________ of the point. The _________________________ between points A and B is the ____________________ _________________ of the difference of their coordinates, or ______________. Example 1: Measuring Segment Length What are UV and SV on the number line above? UV= SV= Postulate 1-6: Segment Addition Postulate If three points A, B, and C are ___________________ and B is ___________________ A and C, then AB + BC = AC. Example 2: Using the Segment Addition Postulate Example 3: Comparing Segment Lengths Use the diagram above. Is segment AB congruent to segment DE? Example 4: Using the Midpoint 1.4 Measuring Angles Key Concept: The ___________________ of an angle is the region containing ________________________________________________________________. The ___________________ of an angle is the region containing ________________________________________________________________. Example 1: Naming Angles Key Concept: TYPES OF ANGLES: Acute angle Right angle Between _____ and ______ degrees Exactly _______ degrees Obtuse angle Straight angle Between ________ and _______ degree Exactly _______ degrees Example 2: Measuring and Classifying Angles What are the measures of angles LKH, HKN, and MKH? Classify each angle as acute, right, obtuse, or straight. Congruent Angles: Postulate 1-8 Angle Addition Postulate: If point B is in the __________________________ of ____________________, then __________________________________________________. Example 3: Using the Angle Addition Postulate 1.5 Exploring Angle Pairs Key Concept: Types of Angle Pairs Adjacent angles are two coplanar angles with a common ____________, a common _____________, and ________ common interior points. Vertical angles are two angles whose sides are _________________________ _________________. Complementary angles are two angles whose ____________________________________ ___________ ___________________________________. Each angle is called the complement of the other. Supplementary angles are two angles whose ____________________________________ ___________ ___________________________________. Each angle is called the supplement of the other. Example 1: Identifying Angle Pairs 1. 5 and 4 are _________________ angles. 2. 6 and 5 are _________________ angles. Linear pair: Linear Pair: 3. 1 and 2 are a _____________________. Postulate 1-9 Linear Pair Postulate: If two angles for a linear pair, then they are ______________________. Vocab: Linear Pair: Angle bisector: Example 2: Missing Angle Measures Angles KPL and JPL are a linear pair. What are their measures? Example 3: Using an Angle Bisector to Find Angle Measures In the diagram, bisects WXZ. a. Solve for x and find mWXY. b. Find mYXZ. c. Find mWXZ. 1.7 Midpoint and Distance in the Coordinate Plane Key concept: Formulas: Midpoint on a number line Midpoint on a graph Distance Example 1: Finding the Midpoint 1. Find the coordinate of the midpoint of the segment with the given endpoints: -8 and 12 2. Find the coordinates of the midpoint of CD. Example 2: Finding the Endpoint The coordinates of point S are (9, -3). The midpoint of RS is (6, 10). Find the coordinates of point R. Example 3: Finding Distance Find the distance between the pair of points. If necessary, round to the nearest tenth. C(2, 6), D(10, 8) 1.8 Perimeter, Circumference, and Area Vocab: Perimeter, P: ________ of lengths of all __________ Circumference, C: Perimeter of a _______________ Area, A: number of __________ __________it encloses Key Concept: Formulas Triangle Square Side length s P= Side lengths a, b, and c s Base b, and height h P= c a h A= A= b Rectangle Base b and Circle h Radius r and diameter d height h C= P= b A= C= A= C You can name a circle with the symbol _________. Pi = ______ = ________ = ________ Postulate 1-10: Area Addition Postulate: The area of a region is the ________ _____ _____ ________ of its nonoverlapping parts. Example #1: Perimeter of a Rectangle You want to frame a picture that is 5 in. by 7 in. with a 1in.-wide frame. Example #2: Circumference a) What is the circumference of a circle with radius of 24 m in terms of π? C=2πr C=2π( C= ) a) What is the perimeter of the picture? P = 2b + 2h P=2( )+2( P= ) b) What is the perimeter of the outside edge of the frame? P = 2b + 2h P=2( )+2( P = ) b) What is the circumference of a circle with diameter 24 m to the nearest tenth? C=πd C=π( C= ) Example #3: Perimeter in the Coordinate Plane Example #4: Area of a Rectangle Graph quadrilateral JKLM with vertices J(-3, -3), K(1, -3), L(1, 4), and M(-3, 1). What is the perimeter of JKLM? You are designing a poster that will be 3 yd. wide and 8 ft. high. How much paper do you need to make the poster? Give your answer in square feet. P=J+K+L+M P= 1 yard = ____ feet, so 3 yd. = ______ feet A = bh A=( )( A= ) Example #5: Area of a Circle The diameter of a circle is 14 ft. a) What is the area of the circle in terms of π? d = 14 feet, so r = ________ feet Example #6: Area of an Irregular Shape What is the area of the figure below? A = π 𝑟2 A = π ( )2 A=π( ) A= b) What is the area of the circle using an approximation of π? 2.6 Proving Angles Congruent Theorem 2-1 Vertical Angles Theorem Theorem 2-2 Congruent Supplements Theorem If… Theorem If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent. Then… Theorem 2-3 Congruent Complements Theorem Theorem If… Then… If… Then… If… Then… If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent. Theorem 2-4 Theorem All right angles are congruent. Theorem 2-5 Theorem If two angles are congruent and supplementary, then each is a right angle. 3.1 Lines and Angles Key Concept Parallel and Skew Definition Parallel lines are ________________ lines that do not __________________. The symbol ______ means “________________________. ” Skew lines are ___________________; they are not ___________________ and do not ____________________. Symbols Diagram Parallel planes are planes that do not ____________________. Transversal: Key Concept Alternate interior angles: Same-side interior angles: Alternate exterior angles: Corresponding angles: 3.2 Properties of Parallel Lines Same-Side Interior Angles are _____________________________ Alternate Interior Angles are ______________________________ Corresponding Angles are _________________________________ Alternate Exterior Angles are ______________________________ EXITS EXITS