Section 1.1 Notes. Points - have no size or dimension and named using capital letters A

Transcription

1 Section 1.1 Notes Building Blocks of Geometry Undefined Terms: Points - have no size or dimension and named using capital letters A Lines - have no thickness (1D) and extend forever. Named using 2 points with a double arrow line above it or a small case letter. P Q Planes - have no thickness and also extend forever along a flat surface. Named using at least 3 points that do not lie in a line. A Plane ABC C B Points that lie in a straight line are said to be collinear. Points that lie in a plane are said to be coplanar. How many dimensions?

2 Definitions Segment: part of a line that begins at one point and ends at another point. The points are called the endpoints of the segment. R S How is the segment above named? Ray : part of a line that starts at a point and extends indefinitely in one direction. The point is called the endpoint of the ray. Q D Named with endpoint listed first. QD not DQ How many dimensions do segments and rays have? Opposite rays: If point C lies on line AB between A and B, then ray CA and ray CB are opposite rays.

3 Section 1.1 Postulates 1. The intersection of 2 lines is a...point 2. The intersection of 2 planes is a...line 3. Through any 2 points there is exactly...one line. 4. Through any 3 non-collinear points there is exactly...one plane 5. If 2 points are in a plane, then the line containing them is...in the plane

4 Section 1.2 Notes There are two different types of statements used in geometry. 1) Postulates : statements that are assumed to be true. (also called axiom or creed - these are more building blocks of geometry - they can't be proven true, so we accept them as being true) 2) Theorems : statements that can be proven using previous postulates and theorems. number line - a line that has been set up to correspond w/real #'s. coordinate of a point - the location of a point Length (or distance) of AB - the measure of AB Symbol? congruent figures - figures that have the same size & shape congruent segments - segments that have the same length Does "equal" equal "congruent? betweenness Segment Addition Postulate A B C AB + BC = AC mab + mbc = mac If AB = 7 and BC = 12, then AC = If AB = 20 and BC = 30, then Are these acceptable notations involving measurements and distance? AB = 5 mab = 5 mab = 5 AB = 5 If AB = 4 and AC = 17, then

5 The distance from Rochester to Rosemount along MN State Hwy. 52 is 93 miles. The distance from Rochester to Cannon Falls, which is in between Rochester and Rosemount, is twice as far as the distance from Cannon Falls to Rosemount. Draw a picture to represent the situation, set up an equation, and solve for the distances from Rochester to Cannon Falls, and from Cannon Falls to Rosemount. FIRST Extra Credit Opportunity! 1 point added to your Chapter 1 Test Score... The towns of Harris, Hinckley, and Moose Lake are located along a straight portion of I-35, north of the Twin Cities. Hinckley is between Harris and Moose Lake. The distance from Harris to Moose Lake is 55 miles. The distance from Harris to Hinckley is 1 mile more than 3 times the distance from Hinckley to Moose Lake. Draw a picture to represent the situation, set up an equation and solve for the following distances: Harris to Hinckley and Hinckley to Moose Lake. Section 1.3 Notes Definitions: midpoint - segment bisector - Due by the end of the hour on a FULL sheet of paper with name and all work shown. WORK INDIVIDUALLY!

6 Ex. 2: The endpoints of segment CD are C(-8,-1) and D(2,4). Find the coordinates of the midpoint M. Ex. 3: The midpoint of segment XZ is M(5,-6). One endpoint is X(-3,7). Find the coordinates of endpoint Z. Ex. 4: Find the length of segment GH, with endpoints G(5,-1) and H(-3,6). Round your answer to the nearest hundredth. Section 1.4 Notes: Angles An angle consists of 2 different rays (called the sides of the angle) sharing the same endpoint (called the vertex of the angle). A protractor can be thought of as a geometry ruler. It measures angles, not segments. Angles are measure in degrees( ). Example: m<abc=72 A B C

7 What is m<poq? Angle Congruence Postulate: If 2 angles have equal measures, then the angles are congruent. P Q If m<a = m<b, then If 2 angles are congruent, then they have equal measures. O If, then m<a = m<b Does the size of the angles matter? Types of Angles: a) Straight: An angle that measures 180 b) Right : an angle whose measure = 90. Angle bisector: A ray, segment, or line that divides an angle into two congruent angles. c) Acute : an angle whose measure is between 0 and 90. d) Obtuse : an angle whose measure is between 90 and 180.

8 Angle Addition Postulate If S is in the interior of <PQR, then m<pqs + m<sqr = m<pqr P Q S R P Q S R If m<pqs = 4x + 1, m<sqr = 2x - 3 and m<pqr = 5x + 8, then find x and all three angle measures. N A M L If m<man = 17x + 3, m<mal = 9(x - 3) and m<nal = 3(7x + 2), then find x and all three angles measures.

9 Section 1.5 Notes: Pairs of angles a) Complementary Angles : 2 angles whose measures add to 90. Adjacent angles are angles in a plane that have their vertices and one side in common but no common interior points. b) Supplementary Angles : 2 angles whose measures add to Are the angles on the following pages adjacent? If no, why not? A D 6 7 <ABD and <ABC? B C

10 A new type of angles! They are called VERTICAL ANGLES <1 and <3 are vertical angles. <2 and <4 are vertical angles. Name all pairs of adjacent angles VERTICAL ANGLES are NOT called OPPOSITE ANGLES!!! Name all linear pairs. Theorem: Vertical angles are congruent. If m<1 = 20 and m<3 = 66, find the other angles: c) Linear Pair : angles that share a common vertex, form a line and have one side in common. m<2 = 94 m<4 = 20 m<5 = 94 m< 6 =

11 Two angles form a linear pair. The measure of one angle is 4 times the measure of the other. Set up an equation to represent the situation and find the measure of both angles. Section 1.6 Notes Equiangular Polygon Equilateral Polygon Regular Polygon Convex Polygon Concave Polygon

12 Section 1.7 Notes Perimeter - the distance/length around a 2D figure. Label = units All angles are right angles. Area - the space inside a 2D figure. Label = square units Formulas: Square Rectangle Triangle Circle Area: Perimeter: Ex. 10: JKL has vertices J(1,6), K(6,6), and L(3,2). Find the perimeter of the triangle. Ex. 11: You are using a roller to smooth a lawn. You can roll about 125 sq. yds. in 1 minute. About how many minutes does it take to roll a lawn that is 120 ft. long and 75 ft. wide?

13 Ex. The A of a is 96 sq. in. and its H is 8 in. Find the length of the base. September 05, 2012