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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 _______point_____ indicates a location and has no size. How to Name It Diagram You can represent a point by a ____a dot_ and name it with a _____capital______ A B _______Letter____________. A _line__ is represented by a straight path You can name a line by any _two_ that extends in two _opposite_____ ____points____ on the line, or by a single directions without end and has no ______lowercase______ letter. __thickness___. A line contains infinitely many __many_____. A ____plane_ is represented by a _flat__ surface that extends without _end__ and has no ______thickness_____. A plane contains infinitely many You can name a plane by a ___capital_____ letter or by any three ___points___ in the plane. ____lines___. Points that lie on the same ___line__ are called __collinear_____ ____points__. What are the names of three collinear points? Points _R_, _Q_, and _S_ are collinear. Points and lines that lie in the What are the names of four coplanar ______same__ plane are points? _____coplanar______. _All_ the points Points _R__, Q__, _S__, and V__ are of a __line__ are coplanar. coplanar. ___Space___ is the set of all _____points____ in three dimensions. A _____segment_____ is part of a line You can name a segment by its that consists of two ____endpoints__ and _endpoint_ another ____point_____. all points ____between____ them. A __ray__ is part of a line that consists of the endpoint. You can name a ray by its __endpoint___ and another ___point___ on the ray. The ___order___ of the points indicates the ray’s ____direction____. _Opposite_ __Rays__ are ________ rays You can name opposite rays by their that share the _same__ endpoint and form ___same_ endpoint and __any_ other a __line___. ___point____ on each ray. one ___endpoint____ and all the ____points____ of the line on one side of A ___postulate____ OR _____Axiom____ is an accepted statement or fact. Postulates, like (Please see the table of Postulates 1-1, 1-2, 1-3, and 1-4 below.) __undefined___ terms, are basic building blocks of the ______logical ______ system of geometry. You will use __logical____ ______reasoning ____ to prove general concepts. When you have two or more geometric figures, their __intersection___ is the set of points the ___figures_____ have in ___common______. Postulate Name Description Through any two points there is exactly one __line___. Postulate 1-1 If two distinct lines intersect, then they intersect in exactly Postulate 1-2 Postulate 1-3 Postulate 1-4 one _point_. If two distinct planes __intersect__, then they ___intersect___ in exactly one line. Through any three noncollinear points there is exactly one ___plane___. 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 Theorem If… Then… If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent. 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