1. 8.6 Identify Special Quadrilaterals
8.6
Bell Thinger
Find the value of x.
1.
3.
ANSWER
65
2.
ANSWER
ANSWER
120
70

2. 8.6

3. 8.6
Example 1
Quadrilateral ABCD has at least one pair of opposite
angles congruent. What types of quadrilaterals meet
this condition?
SOLUTION
There are many possibilities.

4. 8.6
Example 2
SOLUTION
The diagram shows AE CE and BE DE . So, the
diagonals bisect each other. By Theorem 8.10, ABCD
is a parallelogram.

5. 8.6
Example 2
Rectangles, rhombuses and squares are also
parallelograms. However, there is no information given
about the side lengths or angle measures of ABCD.
So, you cannot determine whether it is a rectangle, a
rhombus, or a square.
ANSWER
The correct answer is A.

6. 8.6
Example 3
Is enough information given in the
diagram to show that quadrilateral
PQRS is an isosceles trapezoid?
Explain.
SOLUTION
STEP 1
Show that PQRS is a trapezoid. R and S are
supplementary, but P and S are not. So, PS QR
, but PQ is not parallel to SR . By definition, PQRS is a
trapezoid.

7. 8.6
Example 3
STEP 2
Show that trapezoid PQRS is isosceles. P and S
are a pair of congruent base angles. So, PQRS is an
isosceles trapezoid by Theorem 8.15.
ANSWER
Yes, the diagram is sufficient to show that PQRS is an
isosceles trapezoid.

8. 8.6
1.
Guided Practice
Quadrilateral DEFG has at least one pair of
opposite sides congruent. What types of
quadrilaterals meet this condition?
ANSWER
Parallelogram, Rectangle, Square, Rhombus, Tr
apezoid.

9. 8.6
Guided Practice
Give the most specific name for the quadrilateral.
Explain your reasoning.
ANSWER
Kite: there are two pairs of consecutive congruent
sides.

10. 8.6
Guided Practice
Give the most specific name for the quadrilateral.
Explain your reasoning.
ANSWER
Trapezoid: there is one pair of parallel sides.

11. 8.6
Guided Practice
Give the most specific name for the quadrilateral.
Explain your reasoning.
ANSWER
Quadrilateral; there is not enough information to
be more specific.

12. 8.6
Guided Practice
5. ERROR ANALYSIS: A student knows the following
information about quadrilateral MNPQ:
MN
PQ , MP NQ , and P
Q. The student
concludes that MNPQ is an isosceles trapezoid.
Explain why the student cannot make this
conclusion.
ANSWER
It’s possible that MNPQ could be a rectangle or a
square since you don’t know the relationship
between MQ and NP.

13. Exit
8.6 Slip
Write true or false.
1.
The diagonals of a rectangle are always perpendicular.
ANSWER
2.
False
The diagonals of a rhombus are always congruent.
ANSWER
False
3. One pair of opposite angles of a kite are congruent.
ANSWER
True

14. Exit
8.6 Slip
4. Give the most specific name for the quadrilateral.
Explain.
ANSWER
Rhombus ;
It is a
since two pairs of opp.
s
are = .
Since two consec. sides are = , all sides are = .

15. Exit
8.6 Slip
5. Points A(1, 4), B(6, –1), C(1, –6), D(–4, –1) are the
vertices of a quadrilateral. Give the most specific
name for ABCD. Explain.
ANSWER
Square; slope of AB = slope of CD = – 1, slope of BC =
slope of AD = 1. Opp. sides are = so, ABCD is a
.
Two consec. sides are and AB = BC = 5 2, so ABCD
is a square.

16. 8.6
Pg 572
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