Angles Angle and Points An Angle is a

Angle and Points An Angle is a figure formed by two rays with a

Naming an Angle Using 3 points: Vertex must be the middle letter This angle

Example Name all the angles in the diagram below K is the vertex of

Example Name three angles in the diagram.

4 Types of Angles Acute Angle: an angle whose measure is less than 90.

Angle Addition Postulate Same idea as the segment addition postulate Postulate: The sum of

Example Fill in the blanks. m < ______ + m < ______ = m

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

Example K is interior to MRW, m MRK = (3 x) , m KRW

Example Given that m< LKN = 145, find m < LKM and m <

Example Given that < KLM is a straight angle, find m < KLN and

Example Given m < EFG is a right angle, find m < EFH and

Angle Bisector An angle bisector is a ray in the interior of an angle

Congruent Angles Definition: If two angles have the same measure, then they are congruent.

Example: is an angle bisector J T Which two angles are congruent? <JUK and

Example: Given bisects < XYZ and m < XYW = . Find m <

Example: Given bisects < ABC. Find m < ABC

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Angles

Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. ray vertex ray Angles can have points in the interior, in the exterior or on the angle. B is the vertex. Points A, B and C are on the angle. D is in the interior E is in the exterior. E B A D C

Naming an Angle Using 3 points: Vertex must be the middle letter This angle can be named as Using 1 point: Using only vertex letter Using a number: A Use the notation m 2, meaning the measure of 2. B C

Example Name all the angles in the diagram below K is the vertex of more than one angle. Therefore, there is NO in this diagram.

Example Name three angles in the diagram.

4 Types of Angles Acute Angle: an angle whose measure is less than 90. Right Angle: an angle whose measure is exactly 90 . Obtuse Angle: Straight Angle: an angle whose measure is between 90 and 180. an angle that is exactly 180 .

Angle Addition Postulate Same idea as the segment addition postulate Postulate: The sum of the two smaller angles will always equal the measure of the larger angle. Complete: MRK+ m ____ KRW= m MRW m _____

Example Fill in the blanks. m < ______ + m < ______ = m < _______

Adding Angles If you add m 1 + m 2, what is your result? m 1 + m 2 = 58. Also… m 1 + m 2 = m ADC Therefore, m ADC = 58.

Example K is interior to MRW, m MRK = (3 x) , m KRW = (x + 6) and m MRW = 90º. Find m MRK. First, draw it! 3 x + 6 = 90 4 x + 6 = 90 – 6 = – 6 4 x = 84 x = 21 3 x x+6 Are we done? m MRK = 3 x = 3 • 21 = 63º

Example Given that m< LKN = 145, find m < LKM and m < MKN

Example Given that < KLM is a straight angle, find m < KLN and m < NLM

Example Given m < EFG is a right angle, find m < EFH and m < HFG

Angle Bisector An angle bisector is a ray in the interior of an angle that splits the angle into two congruent angles. 5 3

Congruent Angles Definition: If two angles have the same measure, then they are congruent. Congruent angles are marked with the same number of “arcs”. 3 3 5. 5

Example: is an angle bisector J T Which two angles are congruent? <JUK and < KUT or < 4 and < 6

Example: Given bisects < XYZ and m < XYW = . Find m < XYZ

Example: Given bisects < ABC. Find m < ABC