trapezoids april 29, 2008. what is a trapezoid? a quadrilateral with exactly one pair of parallel...
TRANSCRIPT
What is a trapezoid?
• A quadrilateral with exactly one pair of parallel sides is called a trapezoid. The parallel sides are called the bases and the other sides are called the legs.
More about trapezoids
• Notice that we can prove that exactly one pair of opposite sides of the quadrilateral above are parallel.
• We have two lines cut by a transversal so that same side interior angles are supplementary.
• The bases are the two parallel sides, not top and bottom.
Isosceles Trapezoids
• A trapezoid with congruent legs is called an isosceles trapezoid.
• If you cut out an isosceles trapezoid from a piece of paper and fold it over so that the legs coincide, you will find the both pair of base angles are congruent.
Theorem: The base angles of an isosceles trapezoid are congruent.
• How would you show that angle A and angle B are congruent?
Diagonals of an isosceles trapezoid
• What do you notice about the diagonals of the isosceles trapezoid?
Median of a Trapezoid
• The median of a trapezoid is the segment that joins the midpoints of the legs.
• The median of a trapezoid is very similar to the midsegment of a triangle in that both join the midpoints of sides.
Theorem: The median of a trapezoid
The median of a trapezoid…• is parallel to the bases;• has a length equal to the average of the
base lengths (i.e. 1/2 the sum of the lengths of the bases)
Finding angle measures in an isosceles trapezoid
• Two congruent angles of an isosceles trapezoid have measures 3x + 10 and 5x -10. Find the value of x and then give the measures of all angles of the trapezoid.
Summary
• In summary, a trapezoid is a special quadrilateral in which exactly one pair of opposite sides is parallel.
• This, of course, means that a trapezoid is never a parallelogram since a parallelogram must have both pairs of opposite sides parallel.
• An isosclele trapezoid is a trapezoid in which the legs are congruent ( which in turn means that the base angle and the diagonals are also congruent.).