1- 4 Angles

A) Terms 1) Angle – consists of 2 different rays that have the same endpoint. a) rays are called the sides b) the endpoint is called the vertex c) angles are measured in degrees using a protractor. d) symbol for angle: “<“ e) measure <B denote: m<B or measure <ABC denote: m<ABC f) congruent angles are angles that have the same measure. denote: <ABC <DEF

C) Other Terms: 1) A point is in the interior of an angle it it is between the 2 rays or inside the angle. 2) A point is in the exterior of an angle if it lies outside the angle. Ex. exterior interior

3) Classify Angles: a) Acute Angle - measures less than 90°. b) Right Angle – measures 90° c) Obtuse Angle – measures between 90° and 180°. d) Straight Angle – measures 180° Ex. Label the Angles below. 1) 2) 3) 4)

4) Two angles are Adjacent angles if they share a common vertex and side, but have no common interior points. Ex. A C B D <ABC is adjacent to <CBD

5) Angle Bisector - is a ray that divides the angle in half Ex. Find x. BC bisects <ABD. <ABC = x + 3 and <CBD = 3x – 1.

B) Postulates 1) Postulate 3: Protractor Postulate - The measure of angles are from 0° to 180°.

2) Postulate 4: Angle Addition Postulate If P is in the interior of <RST, then m<RSP + m<PST = m<RST Ex. R m<RSP P m<RST S m<PST T