Wednesday, October 22, 2008
Section 3.5
Section 3.5 was about how you can prove that lines are parallel. You can prove that lines are parallel in many ways. One way is to use all of the converses that are in the dyno that we went over. They are corresponding, alternate exterior, and alternate interior converse. Also if the consecutive interior angles are supplementary then the line would be parallel. These are the ways to prove that lines are parallel.
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Section 3.6
Perpendiculars and Distance
Key Concepts:
The distance from a line to a point not on the line is the length of the segment perpendicular to the line from the point.
The distance between 2 parallel lines is the distance between one of the lines and any point on the other line.
2 lines in a plane are parallel if they are everywhere equidistant. Equidistant means that the distance between two lines measured along a perpendicular line to the lines is always the same. The distance between parallel lines is the length of the perpendicular segment with endpoints that lie on each of the 2 lines.
Theorem 3.9- In a plane, if two lines are equidistant from a third line, then the two lines are parallel to each other.
Section 6.2 !
Parallelogram: A quadrilateral with both pairs of opposite sides parallel.
Theorems:
Opposite sides of a parallelogram are congruent- Opp. sides of parallelograms are congruent
Opposite angles in a parallelogram are congruent- Opp. angles of parallelograms are congruent
Consecutive angles in a parallelogram are supplementary- Consecutive angles in parallelograms are suppl.
If a parallelogram has one right angle, it has 4 right angles- If a parallelogram has one right angle, it has 4 right angles
Remember!
The diagonals of a parallelogram always bisect each other.
and
Each diagonal of a parallelogram separates the parallelogram into two congruent triangles.
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