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Geometry for School and Home
Activity 3.8
Assignment 3.9
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Assignment 9.18
Coordinate Geometry Proof (Slopes and Midpoints)
Objective
Use formulas for slopes and midpoints to demonstrate algebraic proofs of theorems about triangles and quadrilaterals.
End of Unit
About Geometry Worksheet Assignment 9.18:
Assignment 9.18 is an introduction to using the slope and midpoint formulas to complete algebraic proofs of geometry theorems about segments in certain triangles and quadrilaterals.
Prerequisite Skills: Find the slope of a line segment having algebraic coordinates for its endpoints (Assignment 9.9). Find the coordinates of midpoints of line segments with algebraic coordinates for the endpoints (Assignment 9.13). Write algebraic coordinates for vertices and midpoints of sides of certain triangles and quadrilaterals (Assignment 9.16).
Theorems: A midsegment of a triangle is parallel to a side of the triangle.
The line segments with endpoints at the midpoints of the sides of a quadrilateral make a parallelogram.
The diagonals of a square are perpendicular.
The diagonals of a parallelogram bisect each other.