Aim: How do we work with mid-segments and midpoints? Goal: Everyone will understand how to solve and find midpoints and mid- segments.

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Presentation transcript:

Aim: How do we work with mid-segments and midpoints? Goal: Everyone will understand how to solve and find midpoints and midsegments

DEFINITION: Midpoint: Is the point halfway between the endpoints of a line segment. It divides a line segment into two equal segments. Mid-segment of a triangle: Is a segment joining the midpoints of two sides of a triangle.

Midpoints When finding the coordinates of the midpoint of a segment, you are actually finding the average (mean) of the x-coordinates and the average (mean) of the y-coordinates. Formula:

Mid-Segment Properties The mid-segment of a triangle joins the midpoints of two sides of a triangle such that its length is half the length of the third side of the triangle. The mid-segment is parallel to the third side of the triangle. DE ||AB midsegment

Example: Given DE is the length of the mid-segment. Find AB Solution: The mid-segment is half of the third side.7 is half of 14. AB = 14.

Second Example: The mid-segment is half of the third side. 6 is half of 12 so AC = 12 7 is half of 14 so CB = 14 8 is half of 16 so AB = 16 The perimeter of the large triangle ABC is: = 42.

Solve: Find DE Answer:16: Explanation: Line segment DE is half of line segment AB and line AB is 32 which makes Line segment equal to 16. Answer:64 Explanation: line segment DE is 32 and since its half of AB then you just double that number to get AB which is 64. Find AB

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