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©1998 ThinkQuest
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©1998 ThinkQuest
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Chapter 3: Polygons and Their Relations
When comes to determine whether a parallelogram is a rectangle, a square, or a rhombus, we use following theorems:
A parallelogram with one
right angle is a rectangle.
A parallelogram with two
adjacent congruent sides is a rhombus.
A parallelogram with
perpendicular diagonals is a rhombus.
A parallelogram with
congruent diagonals is a rectangle.
A parallelogram with a
diagonal that bisects opposite angles is a rhombus.
A quadrilateral with
four congruent sides is a rhombus.
A special kind of quadrilateral that has one pair of sides parallel is called trapezoid. The altitude of a trapezoid is a perpendicular segment from any point on one base to the line containing the other base. The median of a trapezoid is the segment that joins the midpoints of the legs. Trapezoids also have following properties:
All altitudes of a
trapezoid are congruent.
The median of a trapezoid
is parallel to its bases. Its length is half the sum of the lengths of the two bases.
A special kind of trapezoid is call isosceles trapezoid. An isosceles trapezoid is a trapezoid with congruent legs. Isosceles trapezoids also have following properties:
The base angles of an
isosceles trapezoid are congruent.
If the base angles of a
trapezoid are congruent, then the trapezoid is isosceles.
The diagonals of an
isosceles trapezoid are congruent.
If the diagonals of a
trapezoid are congruent, then the trapezoid is isosceles.
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