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• Sequence (day 1) – Use classroom ex • Types of angles, naming, adj, – Interior of angle – Postulate – Class exercises Day 2 – Adj / bisector – Class ex – Assumptions (day 2) Warm - up • Draw the following and create your own intersection – Line AB and line t intersecting – Plane Q and line XY intersecting – Plane K and plane M intersecting ***THERE ARE PAPERS TO PASS BACK! PASS THEM OUT FOR EXTRA CREDIT 1.4 ANGLES An angle is a geometric figure that consists of two rays that share a common endpoint. The common endpoint of the two rays is called the vertex of the angle The two rays are called the sides of the angle. Naming an Angle A B 1 C L ABC or L CBA OR L B or L 1 This confusing… A B C D • Can we use just the vertex to name these angles? How many angles are there? A B 1 3 2 C D Name the vertex of 3 State another name for 3 State another name for 1 B 2 3 4 A 1 9 8 E 7 6 D 5 C Angle Measurements • We measure the size of an angle using degrees. • We measure the size of an angle using a protractor HOW DO WE USE A PROTRACTOR? Questions 7 - 12 Right Angle A right angle is an angle measuring exactly 90 degrees. You use a protractor to measure angles. This angle measures 90 degrees. It is a right angle. Acute Angle An acute angle is an angle measuring between 0 and 90 degrees. This angle is less than 90 degrees. It is called an acute angle. “Ohhhh look at how a cute the little angle is…..” Obtuse Angle An obtuse angle is an angle measuring between 90 and 180 degrees. This angle is greater than 90 degrees. It is called an obtuse angle. Straight Angle • A straight angle is 180 degrees. A straight angle Is a straight _____? Congruent Angles • Angles that have equal measure Definition: Adjacent Angles Two angles in a plane that have.. 1. a common vertex 2. and a common side but no common interior points. Common Side No Common interior Points Common Vertex T – Adjacent F – Not adjacent 2 1 T – Adjacent F – Not adjacent 2 1 T – Adjacent F – Not adjacent 1 2 T – Adjacent F – Not adjacent 1 2 Bisector of a segment • A line, segment, ray or plane that intersects the segment at its midpoint. 3 3 A B P Something that is going to cut directly through the midpoint Definition: Angle Bisector • The ray that divides an angle into two congruent adjacent angles B BX bisects L ABC Name the two congruent angles C X A Angle Addition Postulate • If point B lies in the interior of AOC, – then m AOB + m BOC = m AOC. – What is the interior of an angle? If AOC is a straight angle and B is any point not on AC, then m AOB + m BOC = 180. Why does it add up to 180? Assumptions • There are certain things that you can conclude from a diagram and others that you can’t. What can you Assume? A D Be Careful B C E What you can Assume? 1. 2. 3. 4. 5. All points shown are coplanar A, B, C are collinear B is between A and C ABC is a straight angle D is in the interior of ABE A D B 6. ABD and DBE are adjacent angles. C E What you can’t Assume? • AB BC • ABD DBE • CBE is a right angle A D B C E Arc marks – indicate congruent angles A D Tick marks – indicate congruent segments B E Indicates a 90 degree angle C Marks are used to indicate conclusions about size in a diagram. Lessons Learned… 1. Don’t Assume ! 2. Follow this rule: You can draw conclusions about position, but not about size. 3. Use markings to help you find out information about the diagram • • • • • B 2 3 4 A 1 9 8 E 7 6 D Name the right angle State another name for 6 State another name for 2 State another name for 9 Name the angle adjacent to 4 that is not 3 5 C