Identify quadrilaterals

1
Identify quadrilaterals
Example 1
Quadrilateral ABCD has both pairs of opposite
sides congruent. What types of quadrilaterals
meet this condition?
Solution
There are many possibilities.
parallelogram
square
rectangle
rhombus
2
Checkpoint. Complete the following exercises.

• Quadrilateral JKLM has both pairs of opposite
  angles congruent. What types of quadrilaterals
  meet this condition?

square
rectangle
parallelogram
rhombus
3
Classify a quadrilateral
Example 2
What is the most specific name for quadrilateral
ABCD?
Solution
The diagram shows that both pairs of opposite
sides are congruent. By Theorem 5.22, ABCD is a
_____________.
parallelogram
rhombus
All sides are congruent, so ABCD is a _________
by definition.
Squares
_______ are also rhombuses. However, there is no
information given about the angle measures of
ABCD. So, you cannot determine whether it is a
________.
square
4
Identify a quadrilateral
Example 3
Is enough information given in the diagram to
show that quadrilateral FGHJ is an isosceles
trapezoid? Explain.
Solution
trapezoid
Step 1
supplementary
parallel
trapezoid
By definition, FGHJ is a _____________.
isosceles
Step 2
base angles
isosceles trapezoid
Yes, the diagram is sufficient to show that FGHJ
is an isosceles trapezoid.
5
Checkpoint. Complete the following exercises.

• What is the most specific name for quadrilateral
  QRST? Explain your reasoning.

A kite. By definition it is a quadrilateral with
2 pair of consecutive congruent sides.
6
Checkpoint. Complete the following exercises.

• Is enough information given in the diagram to
  show that quadrilateral BCDE is a rectangle?
  Explain.

Both pairs of opposite angles are congruent, so
BCDE is a parallelogram by Theorem 5.23.
By definition, BCDE is a rectangle and yes we
have enough information.
7
Pg. 345, 5.12 1-24