5.12 Identify Special Quadrilaterals

Example 1 Identify quadrilateralsIdentify quadrilateralsQuadrilateral ABCD has both pairs of opposite sides congruent. What types of quadrilaterals meet this condition?SolutionThere are many possibilities.

Opposite sides are congruent.

parallelogram rectangle

All sides are congruent.

rhombus square

5.12 Identify Special QuadrilateralsCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 1. Quadrilateral JKLM has both pairs of opposite angles

congruent. What types of quadrilaterals meet this condition?

parallelogram rhombus

Opposite angles are congruent.

rectangle square

All angles are congruent.

5.12 Identify Special Quadrilaterals

Example 2 Classify a quadrilateralClassify a quadrilateralWhat is the most specific name for quadrilateral ABCD?SolutionThe diagram shows that both pairs of opposite sides are congruent. By Theorem 5.22, ABCD is a _____________.

A

D

B

C

parallelogramAll 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

Show that trapezoid FGHJ is __________. F and G are a pair of congruent ____________. So, FGHJ is an _____________________ by Theorem 5.30.

Show that FGHJ is a ___________. G and H are _______________ but F and G are not.

5.12 Identify Special Quadrilaterals

Example 3 Identify a quadrilateralIdentify a quadrilateralIs enough information given in the diagram to show that quadrilateral FGHJ is an isosceles trapezoid? Explain.Solution

F

J

G

H

o102 o102

o78

Step 1 trapezoidsupplementary

.GH to________not is FJbut ____,____ So, FG

Step 2 isoscelesbase angles

HJ parallelBy definition, FGHJ is a _____________.trapezoid

isosceles trapezoid

Yes, the diagram is sufficient to show that FGHJ is an isosceles trapezoid.

5.12 Identify Special QuadrilateralsCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 2. What is the most specific name

for quadrilateral QRST? Explain your reasoning.

Q

T

R

S

7

7

8

8

A kite. By definition it is a quadrilateral with 2 pair of consecutive congruent sides.

5.12 Identify Special QuadrilateralsCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 3. 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 .90D omBoth 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.

5.12 Identify Special Quadrilaterals

Pg. 345, 5.12 #1-24