1 / 14

180 likes | 397 Vues

Geometry Unit 1: Angles. ANGLES 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. A. E. D. B. C.

Télécharger la présentation
## Geometry Unit 1: Angles

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**ANGLES 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. A E D B C Example: Points A, B and C are on the angle. D is in the interior and E is in the exterior. B is the vertex.**3 Ways to name an angle**• We can name an angle using: • Using 3 points • Using 1 point • Using a number**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 *Use this method is permitted when the vertex point is the vertex of one and only one angle. Since B is the vertex of only this angle, this can also be called . A C B**Naming an Angle - continued**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 named as . A B 2 C * 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.**Example**• K is the vertex of more than one angle. Therefore, there is NO in this diagram. There is**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: an angle whose measure is between 90° and 180°. Straight Angle: an angle that is exactly 180°.**Measuring Angles**• Just as we can measure segments, we can also measure angles. • We use units called degrees to measure angles. • A circle measures _____ • A (semi) half-circle measures _____ • A quarter-circle measures _____ • One degree is the angle measure of 1/360th of a circle. 360º 180º 90º**Adding Angles**• When you want to add angles, use the notation m1, meaning the measure of 1. If you add m1 + m2, what is your result? • m1 + m2 = 58°. m1 + m2 = mADC also. Therefore, mADC = 58°.**Angle Addition Postulate**Postulate: The sum of the two smaller angles will always equal the measure of the larger angle. Complete: m ____ + m ____ = m _____ MRK KRW MRW**Example: Angle Addition**K is interior to MRW, m MRK = (3x), m KRW = (x + 6) and mMRW = 90º. Find mMRK. First, draw it! 3x + x + 6 = 90 4x + 6 = 90 – 6 = –6 4x = 84 x = 21 3x x+6 Are we done? mMRK = 3x = 3•21 = 63º**Angle Bisector**An angle bisector is a ray in the interior of an angle that splits the angle into two congruent angles. Example: Since 4 6, is an angle bisector. 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”. The symbol for congruence is . 3 5 Example: 3 5.**Example…**• Draw your own diagram and answer this question: • If is the angle bisector of PMY and mPML = 87°, then find: • mPMY = _______ • mLMY = _______

More Related