Measuring Angles 1-6

Angles  An angle is formed by two rays with the same endpoint. The rays are the sides of the angle. The endpoint is called the vertex of the angle.

Naming Angles  The sides of the angle shown here are BT and BQ. The vertex is B. You could name the angle B, TBQ, QBT, or 1

Naming Angles  Name 1 in two other ways. AEC CEA E would not be a correct name, as it could name either angle 1 or angle 2.

Degrees  Angles are measured in units called degrees.The symbol “°” is used to indicate degrees. There are 360 degrees in a complete circle. 360°

Degrees  Angles are measured by how many of those degrees they take up. 90° 270° This is a 90° angle You would show this in writing by saying m A=90

Angle Classifications  Angles are classified according to their measures. 0<x°<90 x°=180 90<x°<180 x°= 90 acute rightobtuse straight This box means this is a right angle

Classifying Angles

Congruent Angles Angles with the same measure are congruent angles. If m 1 = m 2 then 1 ≅ 2 Angles can be marked as alike to show they are congruent.

Angle Addition Postulate  If point B is on the interior of ∠ AOC, then m ∠ AOB + m ∠ BOC = m ∠ AOC

1. ∠ RST = 50°, ∠ RSW = 125°, 2. Find the measure of ∠ TSW 50+x= x=75

Identifying Angle Pairs There are several pairs of angles that have special relationships:  Vertical Angles  Adjacent Angles  Complementary Angles  Supplementary Angles

Vertical Angles 1. Two angles whose sides are opposite rays. 2. ∠ 1 & ∠ 2 are vertical angles 3. ∠ 3 & ∠ 4 are vertical angles

Adjacent Angles 1. Two angles who share a common side, a common vertex, and no common interior points. 2. ∠ 1 & ∠ 4 are adjacent angles 3. ∠ 3 & ∠ 2 are adjacent angles 4. ∠ 1 & ∠ 3 are adjacent angles 5. ∠ 2 & ∠ 4 are adjacent angles

Complementary Angles 1. Two angles whose measures equal 90° 2. ∠ XYW+ ∠ WYZ = 90 °

Supplementary Angles 1. Two angles whose measures equal 180° 2. ∠ XYW+ ∠ WYZ = 180 °

Identifying Angle Pairs  Identify the angle pairs: a. Vertical b. Complementary c. Supplementary

Making Conclusions from Diagrams Unless there are markings given, you cannot assume anything.

Making Conclusions from Diagrams  What can you conclude from the following diagram?

Making Conclusions from Diagrams  Can you make the following conclusions based on this diagram? TW ≅ WV? PW ≅ WQ? ∠ TWQ= 90°?TV bisects PQ? W is the midpoint of TV?

Coordinate Plane 1-8

Coordinate Plane

Points are located on a coordinate plane by using an ordered pair. (x,y) called the coordinates. T = ( 5,2 ) R = ( -4,-1 )

Distance Formula D=√(x 2 -x 1 ) 2 + (y 2 -y 1 ) 2 D=√(-4-5) 2 + (-1-2) 2 D=√(-9) 2 + (-3) 2 D=√ D=√90 D= D=9.5 T = ( 5,2 ) R = ( -4,-1 )

Midpoint Formula  Find the midpoint of a segment by averaging the x-coordinates and averaging the y coordinates of the endpoints. x 1 +x 2, y 1 +y 2 2

Finding the Midpoint Find the midpoint. x 1 +x 2, y 1 +y , 5+(-5) 2 10, 0 2 (5,0)

Finding the Midpoint  The endpoints of XY are X(2,-5) and Y(6,13). Find the coordinates of the midpoint.

Finding the Endpoint  The midpoint of AB is M(3,4). One endpoint is A(-3,-2). Find the coordinates of B.

Finding the Endpoint  The midpoint of XY is (4,-6). X is (2,-3). Find the coordinates of Y.

Worksheets  1-6: Complete 1-15  1-8: Complete 1-25  Due Tomorrow