Download Trapezoids - Washington

January 31, 2017
Unit 8 Lesson 8
Trapezoids
"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)
January 31, 2017
Isosceles Trapezoid
- a trapezoid with congruent legs
1. Go to my website (www.tinyurl.com/WrightGeometry)
2. Scroll down to Unit 7, Lesson 8 and select the Isosceles Trapezoid link.
3. Answer the following questions.
a) Are the diagonals always congruent? _________
b) Are the diagonals always perpendicular? ________
c) Do the diagonals always bisect each other? ________
d) Do the diagonals bisect the angles? _________
e) Are there any congruent angles in the isosceles trapezoid?_________
If so, describe which angle pair(s) location.
January 31, 2017
How to explain the properties:
What happens if you extend the legs of the isosceles trapezoid?
We use the Triangle Proportionality Theorem and Angle Addition
Post to show the figure is an ___________________.
From here we can the _________ angles are congruent.
And from there we can show the _____________ are congruent
by using congruent triangles. (ABD and DCA)
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.
January 31, 2017
Median of a Trapezoid
- a segment that connecting the midpoints of the legs
1. Go to my website (www.tinyurl.com/WrightGeometry)
2. Scroll down to Unit 7, Lesson 8 and select the Median of a Trapezoid link
3. Answer the following questions.
a) After looking at the angles, what can we say about the median and bases?
b) How can you describe the length of the median? Give me an equation.
January 31, 2017
Theorem 5-19
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 1:
January 31, 2017
Example 2: Find EF, EG, GH, and HF.
Example 3:
Are the bases of a trapezoid allowed to be congruent? Explain.
Can the diagonals intersect on the median? Explain.
January 31, 2017