Lesson 1-4 Angles

4/30/2019 Definition of an angle An Angle is a figure formed by two rays with a common endpoint, called the vertex ray vertex ray

4/30/2019 Angles and Points 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.

Naming an angle An angle can be named several different ways. 4/30/2019 Naming an angle An angle can be named several different ways. You can always use three points. You can use one point sometimes. You can use a number sometimes.

Using three points One name for this angle is <ABC 4/30/2019 Using three points One name for this angle is <ABC The vertex point MUST be the middle letter You can also name this angle <CBA

4/30/2019 Using one letter Sometimes angles can be named by their vertex letter only You can only use this method if the vertex point is the vertex of ONLY ONE angle Since B is the vertex of only this angle, this can also be called <B

4/30/2019 Using a number Sometimes there is a number written inside the angle close to the vertex This is the name of the angle, not its measurement This angle can also be called <2

When you cannot use one letter to name an angle 4/30/2019 When you cannot use one letter to name an angle If more than one angle has the same vertex point, then you cannot use just the vertex to name the angle In this case, use the three letter name or a number if it is present See this example:

Example K is the vertex of more than one angle. 4/30/2019 Example K is the vertex of more than one angle. Therefore, there is NOT an <K in this diagram. There is <LKM, <PKM and <LKP There is also <2 and <3 BUT THERE IS NOT AN <5!!

Types of Angles There are four different types of angles: 4/30/2019 Types of Angles There are four different types of angles: Acute angle: an angle whose measure is less than 90. Right angle: an angle whose measure is exactly 90 .

Types of Angles between 90 and 180. exactly 180 . 4/30/2019 Types of Angles Obtuse angle: an angle that is between 90 and 180. Straight angle: an angle that is exactly 180 .

4/30/2019 Adding Angles When you want to add angles, use the notation m<1, meaning the measure of <1. If you add m<1 + m<2, what is your result? m<1 + m<2 = 58. m<1 + m<2 = m<ADC also. Therefore, m<ADC = 58.

Angle Addition Postulate 4/30/2019 Angle Addition Postulate That last example is an example of the Angle Addition Postulate. This postulate states that the sum of the two smaller angles will always equal the measure of the larger angle. Complete: m< ____ + m< ____ = m< _____ MRK KRW MRW

4/30/2019 Angle Bisector What if a ray in the interior of an angle splits the angle into two congruent angles? This ray would be called an Angle Bisector. Since <4  <6, then is an angle bisector.

Example Draw your own diagram and answer this question: 4/30/2019 Example Draw your own diagram and answer this question: If is an angle bisector of <PMY and m<PML = 87, then find: m<PMY = _______ m<LMY = _______