1. Objective 1.01 Apply the properties and definitions of lines and angles to model and solve problems. Vocabulary Acute: an angle that measure less than 90° Adjacent Angles: two angles that share both a side and a vertex Alternate Exterior: two exterior angles on opposite sides of a transversal which lie on different parallel lines Alternate Interior: two interior angles on opposite sides of a transversal which lie on different parallel lines Angle: two rays sharing a common endpoint Bisector: the point or the line that divides the object or shape into two equal or congruent parts Collinear: points that lie on the same line Complementary: two angles whose sum is 90° Congruence: figures or angles that have the same size and shape Constructions: the drawing of geometric items such as lines, angles and circles using a straightedge/ruler, protractor and compass Coplanar: lying in the same plane

2. Objective 1.01 Apply the properties and definitions of lines and angles to model and solve problems. Vocabulary cont’d Corresponding: two nonadjacent angles on the same side of a transversal such that one is an exterior angle and the other is an interior angle Degree: the unit of measure of an angle Distance: how far apart objects are (can be similar to length) Endpoint: the 'point' at which a line or a curve ends. Length: how long objects are (can be similar to distance) Line: straight path connecting two points and extending beyond the points in both directions Linear Pair: a pair of adjacent and supplementary angles formed by intersecting lines Midpoint: the point halfway between two given points Noncollinear: points that do not all lie on the same line. Obtuse: an angle that has measure more than 90° and less than 180° Parallel: two distinct coplanar lines that do not intersect (have the same slope) Perpendicular: two distinct coplanar intersecting lines that create four 90° angles (have slopes that are negative reciprocals) Plane: a flat surface extending in all directions Ray: a part of a line starting at a particular point and extending infinitely in one direction

3. Reflex: an angle measuring more than 180° but less than 360° Right: an angle measuring exactly 90° Same-Side Interior: two interior angles on same side of a transversal Segment: all points between two given points (including the given points themselves) Side of an Angle: either of the two rays making up an angle (aka edge) Similar: identical in shape, although not necessarily the same size Slope: a number which is used to indicate the steepness of a line, as well as indicating whether the line is tilted uphill or downhill Straight: an angle measuring exactly 180° Supplementary: two angles whose sum is 180° Transversal: a line that cuts across a set of lines or the sides of a plane figure Vertical: angles opposite one another at the intersection of two lines (congruent) Vertex: where the two rays making up the angle meet Objective 1.01 Apply the properties and definitions of lines and angles to model and solve problems. Vocabulary cont’d

4. Goals For This Lesson To identify properties of lines and angles To label parts of a line and angle To understand the angle theorems related to parallel lines To apply the theorems to find angle measurements when given the measurement of some angle To discover learning by comparing angle measurements and types of angles To encourage independent learning as well as working cooperatively in groups

5. Points A point has no length or width, it just specifies an exact location, labeled with a number or letter. Example: The following is a diagram of points A, B, C, and Q:

6. Lines A line extends forever in both directions with infinite points. A line is named using two different points like "line AB" or as. Example: The following is a diagram of two lines: line AB and line HG.

7. Intersection The term intersect is used when lines, rays, line segments or figures meet, that is, they share a common point. The point they share is called the point of intersection. Example: In the diagram below, line AB and line GH intersect at point D: line 1 intersects the square in points M and N: Example: In the diagram below, line 2 intersects the circle at point P:

8. Line Segments A line segment does not extend forever, but has two distinct endpoints. A line segment is name using its endpoints like "line segment AB" or. Example: The following is a diagram of two line segments: line segment CD and line segment PN, or simply segment CD and segment PN.

9. Rays A begins at a certain point and extends forever in one direction. The point where the ray begins is known as its endpoint. We write the name of a ray with endpoint A and passing through a point B as "ray AB" or as. Example: The following is a diagram of two rays: ray HG and ray AB.

10. Endpoints An endpoint is a point used to define a line segment or ray. A line segment has two endpoints; a ray has one. Example: The endpoints of line segment DC below are points D and C, and the endpoint of ray MN is point M below:

11. Parallel Lines Two lines in the same plane which never intersect are called parallel lines. If line 1 is parallel to line 2, we write this as line 1 || line 2. When two line segments DC and AB lie on parallel lines, we write this as segment DC || segment AB. Example: Lines 1 and 2 below are parallel. Example: The opposite sides of the rectangle below are parallel. The lines passing through them never meet.

12. Perpendicular Lines Two lines in the same plane which intersect to form four right angles are called perpendicular lines. If line 1 is perpendicular to line 2, we write this as line 1 line 2. When two line segments DC and AB lie on perpendicular lines, we write this as segment DC segment AB. Example: Lines 1 and 2 below are perpendicular. 1 2

13. Independent Practice Problems: Identify and name each item 1. 5. 2.6. 3.7. 4.8. M L K P Q C B 2 1 2 1 C B E D C A B Please get your work checked before moving on. Thank you!

14. Angles When two rays meet, an angle is formed. Angles are measured in degrees using a protractor. 65 degrees is written 65°. The angle of b° shown below is called the angle ABC, or because we can draw the angle by starting at A, moving to B and then to C. b A B Ray  (edge) C  Ray (edge) Vertex 

15. An angle that is less than 90° is called acute. An angle which is exactly 90° is called a right angle and often denoted by a box. The lines are perpendicular. An angle of more than 90° but less than 180° is called obtuse. An angle which is exactly 180° is called a straight angle. An angle of more than 180° but less than 360° is called reflex.

16. Complementary Angles: Two angles with a sum of 90 degrees Supplementary Angles: Two angles with a sum of 180 degrees : congruent angles

17. Same-Side Interior Angles Like supplementary, two angles with a sum of 180 degrees A B A + B = 180 : congruent angles vertical: congruent angles

18. 1. An angle measuring 89° is:A. AcuteB. RightC. ObtuseD. Reflex 2. An angle measuring 234° is:A. AcuteB. ObtuseC. StraightD. Reflex 3. An angle measuring 98° is:A. AcuteB. RightC. ObtuseD. Reflex 4. Which is closest to the size of angle AOB?A. 33°B. 57°C. 123°D. 147° 5. Which is closest to the size of angle COD?A. 41°B. 49°C. 131°D. 169° 6. Which is closest to the size of reflex angle FOE?A. 106°B. 164°C. 254°D. 286° Use for # 4Use for # 5Use for # 6 Independent Practice Problems: Select the letter choice for the best answer. Please get your work checked before moving on. Thank you!

19. Independent Practice Problems: Please get your work checked before moving on. Thank you!