Geo WarmUp Make label a chart and answer

Geo Warm-Up Make & label a chart and answer the question in a complete sentence John, Harry and Phil are married to Sally, Nancy & Arlene, but not necessarily in that order. John, who is Sally’s brother, has 5 children. Nancy who is a certified public accountant wants to wait several years before starting a family. Harry is married to John’s sister. Who is Phil married to?

Solution n John is married to Arlene ¨ n Harry is married to Sally ¨ n (Sally is his sister, he has children and Nancy is waiting to have children) (John’s sister is Sally) Phil is married to Nancy. Sally Nancy Arlene John x x Harry x x Phil x x

1. 1 Building Blocks of Geometry Examples n n There are 3 undefined terms in geometry: point, line, and plane. These terms can be described but they can’t be defined. A point is a “dot”. It has no size, just a location. A point is named by using a capital letter. A

Examples 1. 1 continued n n A line is made up of an infinite number of points and is considered to be straight. To name a line, pick any two points on the line (in any order) and place a ↔ above them. A plane is a flat surface that extends infinitely along its width and length. You represent it with a 4 -sided figure. To name a plane, a script capital letter is used. A B C P

1. 1 continued n Examples A B C Collinear points are points on the same Are the following points collinear? 1) A and B ______ YES 2) A and B and D ___ line. NO ¨ ANY 2 points will 3) A and B and C ____ YES ALWAYS be collinear n D Coplanar points are points on the same plane. ¨ ANY 3 points will ALWAYS be coplanar F E I G H Are the following points coplanar? 1) E and F and G ______ YES 2) E , F , G, H ______ 3) F, G, H, I ____ NO

n A ray is a part of a line that starts at a point called its endpoint, and then extends infinitely in one direction. To name a ray, you need two points. The first point is its endpoint. This indicates where the ray starts. The other point is any other point on the ray. You then put a → symbol above those two points. A B C Ray AB starts at A extends towards point B - another way to say AB is ____AC If you say CA that is a different ray

n A line segment is a part of a line with a beginning and an end. The point at the beginning and the point at the end are called the endpoints. To name a segment you use its endpoints (in either order) then place a − symbol above them. A B C

n congruent Two segments are if they have the same length. The symbol for is congruent to is_____. Never use a congruent symbol with a number!!! n There are 2 ways to write “the length of a segment” ¨ Equal sign ¨ Or m. AB = “m” stands for measure of”

n To bisect an object means to cut it in half. A D ¨ You can bisect an angle C or a line segment B ¨ To show a bisector you mark the congruent parts BD is the angle bisector of < ABC

n A midpoint of a segment is a point that is halfway between the endpoints. A midpoint bisects the segment. A ¨ B is the midpoint of AC ¨ Formula for midpoint B C

1. 1 Summary n Write down in complete sentences and in your own words 3 things that you learned today.

1. 2 Poolroom Math – pick up protractor on front table l. An angle is formed by two rays that share a common endpoint. l. The vertex of the angle is the common endpoint of the two rays. 37º n Angles are measured in degrees. l. Angles that have the same measure are called congruent angles.

1. 2 continued n 49º An angle bisector is a ray that divides an angle into two congruent angles.

1. 2 Continued 3 methods to name an angle 1. Use three points that make up that angle, the vertex must be in the middle C B < ABC or < CBA A 2. Use the number or letter in the interior of the angle <2 2 3. Use a single letter (be careful about other angles) A F

1. 2 continued Complete Example 1 in your notes. One of you will be called to the board. R U 1 V T

1. 2 continued n Complete example #2. Name each angle bisector and the angle it bisects. b) If a) N D A Y C

1. 2 continued A Protractor is a geometric tool used to measure an angle and to draw an angle. Follow the directions on your notes and measure the two angles. After you have measured the angles, follow the directions from Example 3 and draw two angles.

1. 2 Summary n Write down in complete sentences and in your own words 3 things that you learned today.

1. 1 1. 2 Homework Page 33 -34 #2 -15, 18 -27 n Page 42 -44 # 1 -24, 30 -33 n