Coordinate Proofs Properties and Formulas (Ch. 6)

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Proving Quadrilaterals Properties/Formulas flashcards

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12 Terms

1
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Parallelogram

Properties (THE BIG 5):

  • Opposite sides are congruent

  • Opposite sides are parallel

  • Opposite angles are congruent

  • Consecutive angles are supplementary

  • Diagonals bisect each other

To Prove: (ONE of the following)

  • Diagonals bisect each other

  • Both pairs of opposite sides are parallel

  • Both pairs of opposite sides are congruent

  • One pair of opposite sides is parallel and congruent

2
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Rectangle

Properties:

  • The big 5

  • 4 right angles (equiangular)

  • Diagonals are congruent

To Prove: (Prove it is a parallelogram and ONE of the following)

  • One right angle (Opposite recipricol slopes)

  • Diagonals are conrgeunt

3
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Rhombus

Properties:

  • The big 5

  • 2 congruent consecutive sides (equilateral)

  • Diagonals are perpendicular

  • Diagonals bisect opposite angles

To Prove: (Prove it is a parallelogram and ONE of the following)

  • Diagonals are perpendicular

  • 2 adjacent sides are congruent

4
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Square

Properties:

  • The big 5

  • Rectangle with 2 congruent consecutive sides

  • equilateral

  • 4 right angles

  • Diagonals bisect the angles

  • Diagonals are congruent and perpendicular

To Prove:

  • Prove it is a rectangle and that 2 adjacent sides are congruent.

  • Prove it’s a rhombus and has one right angle.

5
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Trapezoid

Properties:

  • Only 2 parallel sides

  • Parallel sides: bases

  • Non-parallel sides: legs

To Prove:

  • Prove that 1 pair of opposite sides are parallel and the other pair of sides are not parallel.

6
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Isosceles trapezoid

Properties:

  • Legs are congruent

  • Base angles are congruent

  • The mid-segment is parallel to the bases

  • The length of the mid-segment is equal to ½ the sum of the lengths of the bases

To Prove: (Prove the figure is a trapezoid and ONE of the following)

  • Legs are congruent

  • Diagonals are congruent

7
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Right Trapezoid

Properties:

  • One leg is perpendicular to the base

To Prove:

  • Prove figure is a trapezoid and one leg is perpendicular to a base.

8
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Kite

Properties:

  • Quadrilateral with 2 pairs of consecutive sides congruent and no opposite sides congruent.

  • Diagonals are perpendicular

To Prove:

  • Prove 2 consecutive sides are congruent and opposite sides are not congruent.

9
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Line segments are congruent → lengths are equal

Distance Formula

d = √(x2 - X1)2 + (Y2 - Y1)2

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Lines are parallel → slopes are equal

Slope Formula

m = (Y2 - Y1)/(X2 - X1)

11
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Line segments bisect each other → midpoints are the same

Midpoint Formula

Mx = X1 + X2/2

My = Y1 + Y2/2

12
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Lines are perpendicular → slopes are negative reciprocals

Slope Formula

m = (Y2 - Y1)/(X2 - X1)