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 two rays are called the sides of the angle. The common endpoint of the two rays is called the vertex of the angle

Naming an Angle A 1 B 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? 1 B 3 C 2 D

Name the vertex of  3 State another name for 3 State another name for 1 B E D C 2 3 4 5 6 7 8 9 1

HOW DO WE USE A PROTRACTOR? 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

This angle measures 90 degrees. It is a right angle. A right angle is an angle measuring exactly 90 degrees. This angle measures 90 degrees. It is a right angle. You use a protractor to measure angles.

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.. a common vertex 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

Something that is going to cut directly through the midpoint Bisector of a segment A line, segment, ray or plane that intersects the segment at its midpoint. A B P 3 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? When explaining what the interior of an angle is, tell them that it is from 0 to the measure of the angle. Once you get to 180 degrees then there is no interior. You can make measurements from either side of the angle because it is straight

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 E C

What you can Assume? 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 ABD and DBE are adjacent angles. A D B E C

What you can’t Assume? AB BC ABD  DBE CBE is a right angle A D B

Marks are used to indicate conclusions about size in a diagram. Arc marks – indicate congruent angles A D Tick marks – indicate congruent segments B E Indicates a 90 degree angle Marks are used to indicate conclusions about size in a diagram. C

Lessons Learned… Don’t Assume ! Follow this rule: You can draw conclusions about position, but not about size. Use markings to help you find out information about the diagram

State another name for 6 State another name for 2 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 A B E D C 2 3 4 5 6 7 8 9 1