Coordinate Midpoint Property

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Presentation transcript:

Coordinate Midpoint Property If 𝑥 1 , 𝑦 1 and 𝑥 2 𝑦 2 are the coordinates of endpoints of a line segment, then the coordinates of the midpoint are: ( 𝑥 2 + 𝑥 1 2 , 𝑦 2 + 𝑦 1 2 ) Find the midpoint of: a. (4,5) and (1,1) b. (-2, 6) and (-6, -4)

Why is the midpoint important? Geography Navigation Many other reasons

Try These: Plot the following sets of points. Find the midpoint between each set: a. (4,5) and (1,1) b. (-2, 6) and (-6, -4) Algebra Review: Given the end point of and midpoint of (4, 4) what is the other endpoint? (Hint: what is the missing variable?)

Time to Switch Gears… Up Next: Angles!

Angles What do you already know about angles? An angle is formed by two rays that share a common endpoint The common endpoint of the two rays is the vertex of the angle. The two rays are the sides of the angle. How can we name this angle?

Naming Angles Name all the angles in the following shapes:

Length of the rays? Does it matter how long the length of each ray is when naming and measuring angles?

The good stuff: Measuring Angles! The measurement of an angle is the smallest amount of rotation about the vertex from one ray to the other. Angles are measured in degrees The measurement of any angle can be between 0° and 180°. Why 180°?

When actually measuring…

Congruent Angles Two angles are congruent angles if and only if they have the same measure. A ray is an angle bisector if it contains the vertex and divides the angle into two congruent angles.

Practice