Measuring Angles 1 -6 Angles An angle

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. This is a 90° angle 90° 270° You would show this in writing by saying m A=90

Angle Classifications Angles are classified according to their measures. This box means this is a right angle 0

Classifying Angles

Congruent 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=125 -50 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. 2. Two angles whose measures equal 180° ∠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°? W is the midpoint of TV? TV bisects PQ?

Coordinate Plane 1 -8

Coordinate Plane

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 T = ( 5, 2 ) R = ( -4, -1 ) D=√(x 2 -x 1)2 + (y 2 -y 1)2 D=√(-4 -5)2 + (-1 -2)2 D=√(-9)2 + (-3)2 D=√ 81 + 9 D=√ 90 D=9. 486832981 D=9. 5

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 2 , y +y 1 2 2

Finding the Midpoint Find the midpoint. x 1+x 2 , y 1+y 2 2 2 3+7 , 5+(-5) 2 2 10 , 0 2 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