Chapter 13 (PDF)
Chapter 13 (PDF)
Chapter 13 (PDF)
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Lesson <strong>13</strong>.4 • Quadrilateral Proofs<br />
Name Period Date<br />
In Exercises 1–6, write a proof of each conjecture on a separate piece of<br />
paper. You may use theorems added to your theorem list through the end<br />
of Lesson <strong>13</strong>.4.<br />
1. The diagonals of a parallelogram bisect each other. (Parallelogram<br />
Diagonals Theorem)<br />
2. If the diagonals of a quadrilateral bisect each other, then the<br />
quadrilateral is a parallelogram. (Converse of the Parallelogram<br />
Diagonals Theorem)<br />
3. The diagonals of a rhombus bisect each other and are perpendicular.<br />
(Rhombus Diagonals Theorem)<br />
4. If the diagonals of a quadrilateral bisect each other and are<br />
perpendicular, then the quadrilateral is a rhombus. (Converse of the<br />
Rhombus Diagonals Theorem)<br />
5. If the base angles on one base of a trapezoid are congruent, then the<br />
trapezoid is isosceles. (Converse of the Isosceles Trapezoid Theorem)<br />
6. If the diagonals of a trapezoid are congruent, then the trapezoid is<br />
isosceles. (Converse of the Isosceles Trapezoid Diagonals Theorem)<br />
In Exercises 7–9, decide if the statement is true or false. If it is true, prove<br />
it. If it is false, give a counterexample.<br />
7. A quadrilateral with one pair of parallel sides and one pair of<br />
congruent angles is a parallelogram.<br />
8. A quadrilateral with one pair of congruent opposite sides and one pair<br />
of parallel sides is a parallelogram.<br />
9. A quadrilateral with one pair of parallel sides and one pair of<br />
congruent opposite angles is a parallelogram.<br />
Discovering Geometry Practice Your Skills CHAPTER <strong>13</strong> 87<br />
©2008 Kendall Hunt Publishing
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