1. Lesson 1-4 Angles Lesson 1-4: Angles

2. Angle and Points

An Angle is a figure formed by two rays with a common endpoint, called thevertex .

Lesson 1-4: Angles vertex ray ray

Angles can have points in the interior, in the exterior or on the angle.

Points A, B and C are on the angle. D is in the interior and E is in the exterior.B is the vertex. A B C D E 3. Naming an angle: (1) Using 3 points(2) Using 1 point(3) Using a number next slide Lesson 1-4: Angles Using 3 points: vertex must be the middle letter This angle can be named as Using 1 point: using only vertex letter * Use this method is permitted when the vertex point is the vertex ofone and only oneangle. SinceBis the vertex ofonlythis angle, this can also be called. A B C 4. Naming an Angle-continued Lesson 1-4: Angles Using a number: A number (without a degree symbol) may be used as the label or name of the angle. This number is placed in the interior of the angle near its vertex. The angle to the left can be namedas. *The 1 letter name is unacceptable when more than one angle has the same vertex point. In this case, use the three letter name or a number if it is present. 2 A B C 5. Example Lesson 1-4: Angles Therefore, there isNO in this diagram. There is

K is the vertex ofmore than oneangle.

6. 4 Types of Angles Lesson 1-4: Angles Acute Angle: an angle whose measure is less than 90 . Right Angle: an angle whose measure is exactly 90 . Obtuse Angle: an angle whose measure is between90 and 180 . Straight Angle: an angle that is exactly 180 . 7. Measuring Angles

Just as we can measure segments, we can also measure angles.

We use units calleddegreesto measure angles.

• A circle measures_____

• A (semi) half-circle measures_____

• A quarter-circle measures_____

• Onedegreeis the angle measure of 1/360th of a circle.

Lesson 1-4: Angles ? ? ? 360 180 90 8. Adding Angles

When you want to add angles, use the notationm 1 , meaning the measure of 1.

If you add m 1 + m 2, what is your result?

m 1 + m 2= 58 .

Lesson 1-4: Angles Therefore, m ADC = 58 . m 1 + m 2 = m ADC also. 9. Angle Addition Postulate Lesson 1-4: Angles The sum of the two smaller angles will always equal the measure of the larger angle . Complete: m____ + m ____ = m_____ MRK KRW MRW Postulate: 10. Example:Angle Addition Lesson 1-4: Angles 3x + x + 6 = 904x + 6 = 90 6 = 6 4x = 84 x = 21 K is interior to MRW, mMRK = (3x) , m KRW = (x + 6) and m MRW =90 .Find m MRK. 3x x+6 Are we done? m MRK = 3x = 3 21 = 63 First, draw it! 11. Angle Bisector

Anangle bisectoris a ray in the interior of an angle that splits the angle into two congruent angles.

Lesson 1-4: Angles 5 3 Example: Since 4 6,is an angle bisector. 12. Congruent Angles Lesson 1-4: Angles 3 5. 5 3 Definition: If two angles have the same measure, then they arecongruent. Congruent angles are marked with the same number of arcs. The symbol for congruence is Example: 13. Example

Draw your own diagram and answer this question:

Ifis the angle bisector of PMY and m PML = 87 , then find:

m PMY = _______

m LMY = _______

Lesson 1-4: Angles