Trapezoids: Properties and Medians, Schemes and Mind Maps of Algebra

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Trapezoids

Unit 8 Lesson 8

"It is hard to convince a high-school student that he will

encounter a lot of problems more difficult than those of

algebra and geometry."

-Edgar Watson Howe

Trapezoid

-a quadrilateral with one pair of parallel sides

The parallel sides are called the bases

The non-parallel sides are called the legs

There are two pairs of base angles (one pair for each base)

1. Place a point E above line K.
2. Place your compass on point E and swing your compass so it intersects line j twice. Label the intersection points A and D.
3. Draw in segment AE and AD.
4. Label the quadrilateral as ABCD.

4. Measure the following: AB = _______ CD = _______

5. Draw in the diagonals for both isosceles trapezoids and

measure:

AC = ___________ BD = ___________

Q 1 : What seems to be true about isosceles trapezoids?

Isosceles Trapezoid Recap:

1. A trapezoid with congruent legs (definition)
2. Both pairs of base angles are congruent (theorem 5-18)
3. Diagonals are congruent.

Median of a Trapezoid

• a segment that connecting the midpoints of the legs

5. Draw in the diagonals of both trapezoids. Q2: Do the diagonals intersect on the median? Will they ever intersect on the median?

Theorem 5- The median of a trapezoid: (1) is parallel to both bases (2) has a length that is equal to the average of the base lengths.

Example 2 : Find EF, EG, GH, and HF.

Example 2:

Are the bases of a trapezoid allowed to be congruent? Explain.