1. Identify Special Quadrilaterals
5.12
Identify Special Quadrilaterals
Example 1
Identify quadrilaterals
Quadrilateral ABCD has both pairs of opposite sides congruent. What types of quadrilaterals meet this condition?
Solution
There are many possibilities.
parallelogram
rectangle
rhombus
square
Opposite sides are congruent.
All sides are congruent.

2. Identify Special Quadrilaterals
5.12
Identify Special Quadrilaterals
Checkpoint. Complete the following exercises.
Quadrilateral JKLM has both pairs of opposite angles congruent. What types of quadrilaterals meet this condition?
parallelogram
rhombus
rectangle
square
Opposite angles are congruent.
All angles are congruent.

3. Identify Special Quadrilaterals
5.12
Identify Special Quadrilaterals
Example 2
Classify a quadrilateral A D B C
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
All sides are congruent, so ABCD is a _________ by definition.
rhombus
_______ are also rhombuses. However, there is no information given about the angle measures of ABCD. So, you cannot determine whether it is a ________.
Squares
square

4. Identify Special Quadrilaterals
5.12
Identify Special Quadrilaterals
Example 3
Identify a quadrilateral
Is enough information given in the diagram to show that quadrilateral FGHJ is an isosceles trapezoid? Explain. F J G H
Solution
Step 1
Show that FGHJ is a ___________. G and H are _______________ but F and G are not.
trapezoid
supplementary
parallel
By definition, FGHJ is a _____________.
trapezoid
Step 2
Show that trapezoid FGHJ is __________. F and G are a pair of congruent ____________. So, FGHJ is an _____________________ by Theorem 5.30.
isosceles
base angles
isosceles trapezoid
Yes, the diagram is sufficient to show that FGHJ is an isosceles trapezoid.

5. Identify Special Quadrilaterals
5.12
Identify Special Quadrilaterals
Checkpoint. Complete the following exercises. Q T R S 7 8
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. Identify Special Quadrilaterals
5.12
Identify Special Quadrilaterals
Checkpoint. Complete the following exercises.
Is enough information given in the diagram to show that quadrilateral BCDE is a rectangle? Explain. B E C D
By Corollary to Theorem 5.16, we know that
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. Identify Special Quadrilaterals
5.12
Identify Special Quadrilaterals
Pg. 345, 5.12 #1-24