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Transcript
Geometry Chapter 1: Points, Lines, Planes and Angles objectives: 1.1 Points, -identify and model points, lines and planes Lines and -identify collinear and coplanar points intersecting lines and planes in space Planes Bell Ringer: Use your knowledge of geometry to write what you know about the following geometric terms. Use one sticky note per word. It is okay to use your textbook for assistance Undefined Terms Point Line Line segment Plane Collinear Coplanar Congruent Intersecting lines 1 Examples Point Line Plane Model Drawn: Named by: Facts Words/Symbols Example ____________________________________________________________________________ Summary: What did we do in class? What did we learn in class? 2 objectives: 1.2 Linear Measure and - compute with measures Precision Bell Ringer: Review vocabulary we discussed in section 1.1. Students will get a paper with one of the terms from section 1.1 written on back. On the front they have to do one portion of the Frayer Model related to the word. Then they need to find their group members, put up the portions and present. The student with the definition is the presenter. Students are encouraged to review section 1.1 Cornell Notes during presentation and make any needed adjustments. Review Terms Line segment Betweenness Congruent Examples Find the measurement of each segment. Assume that the drawing is not to scale. 1. 2. Find x and RS if S is between R and T. 3. 4. Summary: ___________________________________________________________________________ What did we learn today? What questions do I have? Assignment 1.2 page 17, #12-15,22-39 Complete on back of notes 3 1.3 Distance and Midpoints Bell Ringer: objectives: - find the distance between two points - find the midpoint of a segment Algebra Review Slip – Think, Pair, Share Distance on the Number Line Example Use the number line to find each measure. 1. BD 2. DG Distance on a Coordinate Plane Method 1: Find the distance between A(-2, -1) and B(1, 3). Using Pythagorean Theorem Method 2: Using Distance Formula The distance between two points with coordinates ( x1, x 2 ) and ( y1, y 2 ) is d ( x2 x1 ) 2 ( y 2 y1 ) 2 4 Example Find the distance between A(-2, -1) and B(1, 3). Midpoint of a If the coordinates of the endpoints of a segment are a and b, segment then the coordinate of the midpoint of the segment is ab Mid point 2 Segment Bisector Midpoint on the Number Line Use the number line to find the coordinate of Example the midpoint of each segment. 1. CE 2. DG If a segment has endpoints with coordinates ( x1 , y1 ) and ( x2 , y2 ) then the formula for the Midpoint on a Coordinate midpoint is Midpoint = x1 x 2 , y1 y 2 Plane 2 2 Example Find the coordinates of the midpoint of a segment having the given endpoints. E(-2, 6), F(-9, 3) Summary: What did we learn today? What did I already know? What was new? Assignment 1.3 page 25 #13-43 odd 5 objective: -measure and classify angles -identify and use congruent angles and the bisector of an angle 1.4 Angle Measure Bell Ringer: Algebra Review Slip – Think, Pair, Share (Transparency) ray opposite rays angle Protractor and degrees Right angle Acute angle Obtuse angle Types of angles Examples Congruent angles Angle bisectors Assignment 1.4 ____________________________________________________________________________ pg 34 13-27 Summary to be completed on back of notes: What did we learn in class? odd, 35-39 odd 6 Examples 7 objective: 1.5 Angle Relationships -identify and use special pairs of angles Bell Ringer: -identify and use perpendicular lines ____________________________________________________________________________ Show work & answer here (Transparency) Special pairs of angles ____________________________________________________________________________ Adjacent Angles – Vertical Angles – Linear pairs – Complementary Angles – Supplementary Angles – Identify each pair of angles as adjacent, vertical, and/or as a linear pair. 1. 1 and 2 2. 1 and 6 3. 1 and 5 4. 3 and 2 8 Perpendicular Lines Examples 5. Find x, mPQS, and mSQR. Summary: 1) Describe the difference between complementary and supplementary angles in your own words. _______________________________________________________ ________________________________________________________________________ 2) Complete each sentence. a) If two angles are supplementary and x is the measure of one angle, then the measure of the other is _____________. a) If two angles are supplementary and x is the measure of one angle, then the measure of the other is _____________. Assignment 1.5 page 42 #1116,18,23-29 9 objective: -Identify and name polygons -Find perimeters of polygons ____________________________________________________________________________ Bell Ringer: Show work & answer here (Transparency) 1.6 Polygons ____________________________________________________________________________ What is a polygon? Use the picture to answer questions 1 - 6. 1. Name all of the sides of the polygon. 2. Name all of the vertices of the polygon. 3. What is the name of the polygon? 4. Name all of the angles in the polygon. 5. Name all of the diagonals in the polygon. Convex Polygon Concave Polygon Regular Polygon What is the name of a regular quadrilateral? 10 Types of polygons n-gon perimeter What is the name of a 21-sided figure? Examples Find the length of each side of the polygon for the given perimeter. 1. 2. Assignment 1.6 page 49 #12-23, 26, 29-33 11 Examples COORDINATE GEOMETRY Find the perimeter of the polygon below. 3. quadrilateral OPQR with vertices O(-3, 2), P(1, 5), Q(6, 4), and R(5, -2)????? Summary: What did we do in class? What did we learn in class? 12