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17 Cards in this Set
- Front
- Back
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Parallelogram
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A quadrilateral is a parallelogram iff both sides are parallel.
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Rhombus
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A parallelogram is a rhombus iff it has one pair of consecutive, congruent sides.
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Rectangle
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A parallelogram is a rectangle iff it has one right angle.
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Square
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A figure is a square iff it is both a rhombus and a rectangle.
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Kite
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A quadrilateral is a kite iff it has two distinct pairs of consecutive, congruent sides.
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Trapezoid
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A quad. is a trapezoid iff it has exactly one pair of parallel sides.
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Parallelogram Theorem
(you must already know that you have a parallelogram) |
1. Both pairs of opposite sides are congruent.
2. Both pairs of opposite angles are congruent. 3. Consecutive angles are supplementary. 4. Diagonals bisect each other. |
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Diagonal Theorem
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1. Rectangle: Diagonals are congruent.
2. Isoceles trapezoid: diagonals are congruent. 3. Rhombus: diagonals are perpendicular and bisect the angles from which they are drawn. 4. Kite: 1 diagonal is the perpendicular bisector of the other and bisects the angles TO which it is drawn. |
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Isoceles trapezoid theorem
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If a trapezoid is isoceles, then both pairs of base angles are congruent.
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5 WAY THEOREM
A quadrilateral is a parallelogram if any one of the following is true: |
1. Both pairs of opposite sides are parallel.
2. Both pairs of opposite sides are congruent. 3. Both pairs of opposite angles are congruent. 4. 1 pair of opposite sides is both parallel and congruent. 5. The diagonals bisect each other. |
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Point-Line-Plane postulate
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1. a) two points determine a line. b) 3 non-collinear pts determine a plane. 3) 4 non-collinear pts determine space.
2. a) two lines intersect in a single pt. b) 2 planes intersect to make a line. c) 3 planes intersect in a point OR a line. d)a line and a plane intersect in a point. 3. a) thru any 1 pt exists infinite lines. b) thru any one line exists infinite planes. |
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Skew lines
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2 lines are skew if they exist in different planes, do not intersect, and extend in different dimensional directions.
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Perpendicular Line Plane theorem
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A line is perpendicular to a plane iff it is perpendicular to at least two distinct lines in the plane that go through the foot.
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Foot (of a plane)
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The pt at which a plane intersects with a line.
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Formulas for:
1. Total # of Diagonals 2. Sum of the measures of the angles of any polygon 3. Each interior angle of a REGULAR polygon 4. Sum of measures of an exterior angle of any polygon 5. Each exterior angle in a regular polygon |
1. n(n-3)/2
2. (n-2)180 3. (n-2)180/n 4. 360 5. 360/n |
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LOGIC STATEMENTS
1. Conditional 2. Converse 3. Inverse 4. Contrapositive |
1. If P then Q
2. If Q then P 3. If not P then not Q 4. If not Q then not P |
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Biconditional
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if all 4 logic statements are true
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