Download What Are Some Properties of Trapezoids?

Geometry H
Unit 3: Quadrilaterals
Section 5.3
Name: _________________________________
Date: __________________
Period: _______
What Are Some Properties of Trapezoids?
Open Geometer’s Sketchpad, and then go to my outbox and open the sketch titled Definition of
Trapezoid.gsp. Move the polygons around by dragging the vertices. What do you notice about the
characteristics of a trapezoid? After you make some observations, write a definition for trapezoid.
Remember that in a good definition, you must classify your term, differentiate your term and then test
your definition by looking for a counterexample.
Trapezoid: __________________________________________________________________________________
____________________________________________________________________________________________
In a trapezoid, the parallel sides are called the bases. A pair of angles that
share a base as a common side are called base angles.
Sketch:
Step 1: Go into my outbox and open the sketch titled Trapezoid.gsp. You will be using this sketch for
the first part of this investigation.
Step 2: Measure all four angles of the trapezoid.
Investigate:
1. A trapezoid has two pairs of consecutive angles that lie between the bases.
One such pair in the trapezoid to the right is ∠DCB and ∠CBA . What is
the other pair of consecutive angles that lies between the bases?
D
A
2. Rearrange your angle measurements on your sketch to match up these consecutive
pairs. Drag the vertices of the trapezoid and observe the angle pairs. Make
calculations to check your observations and then complete the conjecture below.
C-39 Trapezoid Consecutive Angles Conjecture: The consecutive angles between the bases of a
trapezoid are __________________________.
C
B
A trapezoid whose two nonparallel sides are the same length is called
an isosceles trapezoid. We will now look at some properties of
isosceles trapezoids.
Sketch:
Step 1: Go into my outbox and open the sketch titled Isosceles Trapezoid.gsp. You will be using this
sketch for the rest of this investigation.
Step 2: Measure all four angles of the trapezoid.
Investigate:
1. Drag different vertices of the isosceles trapezoid and observe the angle
measures.
C-40 Isosceles Trapezoid Conjecture: Each pair of base angles of an isosceles trapezoid are
____________________.
2.
Construct the diagonals of the isosceles trapezoid and measure both of their lengths.
Drag vertices of the trapezoid and make observations about their lengths.
C-41 Isosceles Trapezoid Diagonals Conjecture: The diagonals of an isosceles trapezoid are
____________________.
Practice:
1.
x = __________ , y = __________
2. x = __________ , y = __________
3. Perimeter = 111 cm, x = __________
4. x = __________ , y = __________
5. Perimeter PQRS = 220, mPS = __________
6. STOP is an isosceles trapezoid.
What are the coordinates of T?
7.
Find the missing lettered angle measures.
8. Construct an isosceles trapezoid given base AB, angle B and distance between bases XY.