Coordinate Geometry Reference Sheet:
Name:______________________ Date:_____ Period:____
Coordinate Geometry Reference Sheet
Coordinate Geometry Reference Sheet:
General Methods of Proof and Formulas
|To Prove |Formula to Use |
|that line segments are congruent, show that the lengths are equal. |Distance Formula |
| |d = √(x2 – x1)2 + (y2 – y1)2 |
|that line segments bisect each other, show that the midpoints are the |Midpoint Formula |
|same. |M = ( _x1 + x2_ , _ y1 + y2_ ) |
| |2 2 |
|that lines are parallel, show that the slopes are equal. |Slope Formula: _y2 – y1_ |
| |x2 – x1 |
| |m1 = m2 |
|that the lines are perpendicular, show that the slopes are negative |Slope Formula: (see above) |
|reciprocals. |Products of slopes = -1 |
Methods that can be used to Prove that a
Quadrilateral Belongs to a Specific Category:
|To Prove a Figure is a(n) |Methods |
|Parallelogram |Show one of the following: |
| |The diagonals bisect each other |
|Rectangle |Show that the figure is a parallelogram using any one of the four methods above |
| |AND |
| |one of the following: |
| |The diagonals are congruent |
|Rhombus |Show that the figure is a parallelogram using any one of the four methods above |
| |AND |
| |one of the following: |
| |The diagonals are perpendicular |
|Square |Show that the figure is a rectangle |
| |AND |
| |two adjacent sides are congruent |
| |OR |
| |Show that the figure is a rhombus |
| |AND |
| |one angle is a right angle |
|Isosceles Triangle |Show that the figure has two congruent sides |
|Right Triangle |Show that one of the legs is perpendicular to the base of the triangle |
|Trapezoid |Show that the quadrilateral has only one pair of opposite sides parallel |
|Isosceles Trapezoid |Show that the figure is a trapezoid |
| |AND |
| |one of the following: |
| |The diagonals are congruent |
|Right Trapezoid |Show that the figure is a trapezoid |
| |AND |
| |one of the legs is perpendicular to the base of the trapezoid |
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