Presentation on theme: " Congruent Segments – › Line segments that have the same length. Midpoint – › The point that divides a segment into two congruent segments. Segment."— Presentation transcript:
Congruent Segments – › Line segments that have the same length. Midpoint – › The point that divides a segment into two congruent segments. Segment Bisector – › A point, line, ray, segment, or plane that intersects the segment at its midpoint.
M T D C S Segment Bisector (Segment CD) Midpoint (Point M)
When two numeric values are the same, the values are equal. When two geometric figures are the same, the figures are congruent. ST Where is the midpoint of ST? -2 M SM ≅ MT, but their lengths are equal. SM = MT = 4.
Coordinate Geometry is the term used to refer to shapes in the Cartesian coordinate plane. We can use our method of finding our midpoint on a number line and apply it to any segment in the coordinate plane! If point A is (x 1, y 1 ) and point B is (x 2, y 2 ), then…
To find the distance between any two points on the coordinate plane, we can use the Pythagorean Theorem for right triangles: a and b are the legs of the triangle and c is the hypotenuse, or longest side, of the triangle.
When a segment is in the coordinate plane, if it is horizontal or vertical we can simply count the units from endpoint to endpoint to find its distance. (easy!)
When a segment is not horizontal or vertical, we can always draw a right triangle to help us create a formula for finding its length. If we solve for d by taking the square root of both sides, we get our formula!
Given 2 points A(x 1, y 1 ) and B(x 2, y 2 ), we can find the distance D from A to B by plugging the coordinates into the formula where they belong. Distance will always be a positive number. If you end up getting a negative answer, check your work!
This assignment WILL BE COLLECTED for a completion grade! › Day 1: Do Prac. #1-7, 11, 12 (1 st page of file) › Day 2: Do Prac. #13-18, App. #4 Assignment is due Monday, 8/10 (A-Day) or Tuesday, 8/11 (B-Day)