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Name: _________________________________Block:_____________Date: ____________________ Chapter 1 Essentials of Geometry Sections Covered: 1.1 Points, Lines, and Planes 1.2 Segments and Congruence 1.3 Midpoint and Distance Formulas 1.4 Measure and Classify Angles 1.5 Angle Pair Relationships SOL G.3 The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include a) investigating and using formulas for finding distance, midpoint, and slope; Unit 2 Syllabus: Ch 1 Essentials of Geometry Block Date Topic 7 9/22 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence Homework Wkst: 1.1 Definitions and 1.2 Segment Addition Postulate 8 9/24 1.3 Use Midpoint and Distance Formulas Wkst: 1.3 Midpoint and Distance 9 9/26 Review Day Wkst: 1.1-1.3 Review 10 9/30 Quiz 1.1-1.3 Spiral Review 11 10/2 1.4 Measure and Classify Angles Wkst: 1.4 Angle Measurement 12 10/4 1.5 Describe Angle Pair Relationships Wkst: 1.5 Angle Relationships 13 10/6 Review Day Wkst: Chapter 1 Review 14 10/8 Chapter 1 Test Spiral Review ***Syllabus subject to change due to weather, pep rallies, illness, etc Need Help? Mrs. Prusak are available in the morning. Email her to set up a time! Mu Alpha Theta is Monday, Tuesday, Thursday, and Friday mornings in L409. Need to make up a test/quiz? Math Make Up Room is open Tuesday, Thursday, and Friday mornings and Monday, Wednesday, and Thursday afternoons. 2 Notes 1.1 Essential Definitions Definition Diagram Notation 1. Point No dimension A 2. Line One dimension; extends without end l S R 3. Plane Y Two dimensions; extends without end X Z M 4. Line Segment Part of a line that contains two endpoints and all the points between them A B 5. Ray Part of line that consists of the endpoint and all the points on the line that extend in one direction Initial point Beginning point of the ray A C 6. Opposite Rays Rays with same initial point and extend to form a line C A B 7. Collinear points Points that lie on the same line X Y 8. Coplanar points Points that lie on the same plane Y X Z M Intersection: The intersection of two lines is _____________________. The intersection of a line and a plane is ____________________. The intersection of two planes is ________________________. 3 Let’s put these definitions to use and you will be able to see that these really are not that difficult. B C Name this line SEVEN different ways. A Using the same diagram to the right name FOUR rays: Opposite rays: Line segments: m Using the diagram to the right: Name the plane shaded in two different ways. Identify at least FOUR pairs of collinear points. Identify at a set of coplanar points. Where do lines g and h intersect? Where does line g intersect with plane F? 4 Notes 1.2 Segment Additional Postulate Postulate: ______________________________________________________________________ Theorem: ______________________________________________________________________ Segment Addition Postulate: If ________ is between ________ and ________, then __________ + __________ = ___________. Remember: “The ____________ is equal to the ___________________________.” Example: Congruent Segments: segments that have the same __________. a) AB PQ is read "segment AB is _________________ to segment PQ." b) AB = PQ is read "AB equals PQ" or “The length of segment AB equals the length of segment PQ.” c) Since AB and PQ represent numbers, they are equal. In contrast, AB and PQ represent figures and are called congruent. Diagram: Notation: Example: 5 Example: Example: Together On Your Own Example: Point S is between R and T on RT . Us e the given information to write an equation in terms of x. Solve the equation. Then, find RS and ST. a. RS = 2x + 10 ST = x – 4 RT = 21 b. RS = 3x – 16 ST = 4x – 8 RT = 2x + 36 6 Notes 1.3: Midpoint & Distance Midpoint: _______________________________________________________________________________ Segment bisector:_________________________________________________________________________ 1.) Find AC if AB = 10 cm. 2.) Point W bisects UV . Find UV if WV = 14 inches. 3.) Find FM. 4.) Point M is the midpoint of VW . Find the length of VM . PRACTICE: In the diagram, M is the midpoint of the segment. Find the indicated length. a. b. 7 Ex1: Given two endpoints can you FIND THE MIDPOINT? The coordinates of a segment’s midpoint are (______________, ________________) **Think SAD….. The endpoints of AB are A(3, 2) and B(6, 7). Find the coordinates of the midpoint M. Find the coordinates of the midpoint of the segment with the given endpoints. a. S (4, -1) and T (6, 0) b. L (4, 2) and P (0, 2 ) c. H (-5, 5) and K (7, 3) Ex2: Given an endpoint and a midpoint, can you find the other endpoint?. Use the given endpoint R and midpoint M of RS to find the coordinates of the endpoint S. R (1, 2) and M (-2, 1) **Think…. DMSE On Your Own: 8 Ex3: Given two endpoints, can you find the distance? Think… Pythagorean Thm Find the length of the segment. Leave answer in simplest radical form and round to the nearest tenth of a unit. Ex4: Given two endpoints, can you evaluate to see if they are congruent? 9 Notes 1.4: Angle Relationships 1. An angle is a figure formed by 2 __________that have the same endpoint. 2. The rays of the angle are called __________ of the angle; the endpoint is called the ______________. An angle is named three ways: 1) by 3 capital letters, but the vertex must be in the middle. _______ or ________ A 2) by a number placed inside the angle. _________ B 2 C 3) by the vertex...if there is only one angle with that vertex. Even though the angle is named four different ways, it is the same angle. _________ Adjacent angles are 2 angles that 1. 2. 3. 4. Are these angles adjacent? 6 4 1 2 ________ 3 ________ 5 ________ 8 7 _______ 9 10 _______ Definition: Congruent angles are angles that have the same _______________. Reminders… 1. Acute angle- angle with measure between _____ and _____. 2. Right angle- angle with measure of _______. 3. Obtuse angle- angle with measure between _____ and ______. 4. Straight angle- angle with measure of _________. 10 TWO BIG IDEAS (for angles): 1. Angle Bisector Idea: Ex. BT bisects ABC. Find the value of x. Then find the measure of the angles to the nearest tenth. C T (3X + 13) B (5X - 17) A On Your Own: Find x given the following: A. m∠ABC = 98° B. m∠ABC = 9x + 87° 11 2. Angle Addition Postulate: EX: ADC = 50°. What does ADB and BDC equal to the nearest tenth? 12 Notes 1.5: Angle Relationships Vertical Angles: Linear Pair: Adjacent: Determine if the angles are vertical angles, linear pair, or neither. a) b) c) d) e) f) 5 and 6 g) 1 and 4 Classify the angles as linear pair, vertical angles or neither. a) 2, 5 b) 4, 7 c) 8, 10 d) 3, 10 Find the value of each variable to the nearest tenth. Be sure to write an equation and circle the answer. 1. 2. 13 3. 4. Complementary Angles: Supplementary Angles: 1) Find the complement of 27. 2) Find the supplement of 115. 3) The following angles are complementary. Find the measure of the angles to the nearest tenth. mA 5x 4, mB 7x 10 4) The following angles are supplementary. Find the measure of the angles to the nearest tenth. mA 11x 2, mB 8x 7 5) Two angles form a linear pair. The measure of one angle is 8 times the measure of the other angle. Find the measure of each angle to the nearest tenth. 14