6 Mid-Chapter Quiz

Do you know HOW?

Find the value of each variable.

Algebra Find the values of the variables for which ABCD is a parallelogram.

Algebra Classify the quadrilateral. Then find the value(s) of the variable(s).

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9. Find AB, CD, and EF.

   

Classify the quadrilateral as precisely as possible. Explain your reasoning.

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14. In the figure below, A B ↔ ∥ C D ↔ ∥ E F ↔ . modified eh b with left right arrow above , parallel to , modified c d with left right arrow above , parallel to , modified e f with left right arrow above , .

    Find AE.

    

15. Given: ▱ A B C D white parallelogram eh b c d , A C ¯ eh c bar bisects ∠ D A B angle d eh b

    Prove: A C ¯ eh c bar bisects ∠ D C B . angle d c b .

    

Do you UNDERSTAND?

Decide whether the statement is true or false. If true, explain why. If false, show a counterexample.

16. A quadrilateral with congruent diagonals is either an isosceles trapezoid or a rectangle.
17. A quadrilateral with congruent and perpendicular diagonals must be a kite.
18. Each diagonal of a kite bisects two angles of the kite.
19. Reasoning Can you fit all of the interior angles of a quadrilateral around a point without overlap? What about the interior angles of a pentagon? Explain.
20. Writing Explain two ways to show that a parallelogram is a rhombus.
21. Draw a diagram showing the relationships among the special quadrilaterals that you have learned.

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