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Chapter 5 - Geometry
N/a
23
Mathematics
10th Grade
11/16/2012
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Term
Parallelogram
 Definition
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
Term
Theorem 5-1
 Definition
Opposite sides of a parallelogram are congruent.
Term
Theorem 5-2
 Definition
Opposite sides of a parallelogram are parallel.
Term
Theorem 5-3
 Definition
Diagonals of a parallelogram bisect each other.
Term
Theorem 5-4
 Definition
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Term
Theorem 5-5
 Definition
If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.
Term
Theorem 5-6
 Definition
If both pairs of opposite angle of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Term
Theorem 5-7
 Definition
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Term
Theorem 5-8
 Definition
If two lines are parallel, then all points on one line are equidistant from the other lines.
Term
Theorem 5-9
 Definition
If three parallel lines cut of congruent segments on one transversal, then they cut off congruent segments on every transversal.
Term
Theorem 5-10
 Definition
A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.
Term
Theorem 5-11
 Definition
The segment that joins the midpoints of two sides of a triangle:

1) is parallel to the third side;
2) is half as long as the third side.
Term
Rectangle
 Definition
4 right angle
Term
Rhombus
 Definition
4 congruent sides
Term
Square
 Definition
4 right angles and 4 congruent sides
Term
Theorem 5-12
 Definition
The diagonals of a rectangle are congruent.
Term
Theorem 5-13
 Definition
The diagonals of a rhombus are perpendicular.
Term
Theorem 5-14
 Definition
Each diagonal of a rhombus bisects two angles of the rhombus.
Term
Theorem 5-15
 Definition
The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.
Term
Theorem 5-16
 Definition
If an angle of a parallelograms is a right angle, then the parallelogram is a rectangle.
Term
Theorem 5-17
 Definition
If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.
Term
Theorem 5-18
 Definition
Base angles of an isosceles trapezoid are congruent.
Term
Theorem 5-19
 Definition
The median of a trapezoid:

1) is parallel to the bases;
2) has a length equal to the average of the base length.
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