Honors Geometry. Worksheet 4.1: Quadrilaterals. Quadrilateral:. (definition) Parallelogram:. (definition)

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1 Honors Geometry Name: Worksheet 4.1: Quadrilaterals Fill in the blanks using definitions and theorems about quadrilaterals. Quadrilateral:. The midquad of a quadrilateral is a. The sum of the measures of the interior angles is. Parallelogram:. The midquad a parallelogram is a. If a quadrilateral has two pairs of opposite congruent, then it is a parallelogram. If a quadrilateral is a parallelogram, then it has two pairs of opposite congruent. If a quadrilateral has two pairs of opposite congruent, then it is a parallelogram. If a quadrilateral is a parallelogram, then it has two pairs of opposite congruent. If a quadrilateral is a parallelogram, then its diagonals. If the diagonals of a quadrilateral bisect each other, then. If a quadrilateral has one pair of and sides, then it is a parallelogram. If a quadrilateral is a parallelogram, then the angle bisectors of opposite angles are and. Rectangle:. The midquad of a rectangle is a. The angles in a rectangle are all. A rectangle is also a. If a quadrilateral is a rectangle, then its diagonals are. If a quadrilateral is a rectangle, then it is.

2 If a has a right angle, then it is a rectangle. A llogram with congruent is a rectangle. Rhombus:. The midquad of a rhombus is a. A rhombus is also a. If a quadrilateral is a rhombus, then its diagonals are. If a quadrilateral is a rhombus, then its diagonals bisect. If the diagonals of a quadrilateral bisect opposite, then it is a rhombus. If a llogram has a pair of consecutive congruent, then it is a rhombus. Square:. The midquad of a square is a. A square is also a and a. Trapezoid:. Isosceles Trapezoid:. The midquad of an isosceles trapezoid is a. If a trapezoid is isosceles, then it has two pairs of. If a trapezoid is isosceles, then its diagonals are. If a trapezoid is isosceles, then it is. If a trapezoid has a pair of congruent base angles, then. If a trapezoid has congruent diagonals, then.

3 Kite:. The midquad of a kite is a. If a quadrilateral is a kite, then its diagonals are. If a quadrilateral is a kite, then it has one pair of. If a quadrilateral is a kite, then one diagonal. If a quadrilateral is a kite, then one diagonal bisects a pair of. A kite is never a or a. A kite could have,, or right angles. If exactly one diagonal is the of the other diagonal, then the quadrilateral is a kite. Regular n-gon:. The sum of the measures of the angles in a regular n-gon can be found using the expression:. The measure of each angle in a regular n-gon can be found using the expression:. Every regular n-gon is. Determine if the following statements are sometimes, always, or never true. Justify. **As you complete these SANs, you may only utilize the theorems we have PROVEN in the list above. 1. A rectangle is a rhombus. 2. A kite has one pair of parallel sides.

4 3. A quadrilateral with congruent diagonals is a rectangle. 4. A trapezoid has exactly one right angle. 5. A kite has exactly one right angle. 6. Bases of a trapezoid are congruent. Circle the answer(s) that satisfy each statement. There may be more than one answer possible! 7. The following is NOT a property of a rhombus: a. All four sides are congruent b. All four angles are 90 degrees 8. The following is NOT a property of a square: a. Exactly one diagonal bisects the other b. Four congruent sides. 9. The following is the total number of degrees in a heptagon: a. 540 b. 720 c. Two sets of parallel sides d. Diagonals are perpendicular c. Congruent diagonals d. Four right angles c. 900 d The following is the measure of one angle in a regular dodecagon (a 12-gon): a. 108 c. 360 b. 120 d. 150

5 11. If ABCD is a parallelogram, =, and = 2 3, find the value of x. a. 3 c. 61 b. 31 d Opposite angles are always congruent in a(n): a. Trapezoid b. Quadrilateral c. Isosceles trapezoid d. Parallelogram e. All of the above 13. Which of the following guarantees that a quadrilateral is a parallelogram: a. It has one pair of congruent sides. c. The diagonals bisect each other. b. It has one pair of parallel sides. d. The diagonals are congruent. 14. Not all rectangles have: a. Diagonals that bisect each other. b. Diagonals that are congruent. c. Four congruent sides. 15. Diagonals can be congruent in all but the following: a. Rectangle b. Non-square Rhombus d. Supplementary consecutive angles. e. Four congruent angles. c. Square d. Isosceles trapezoid In quadrilateral ABCD, name the most general type of quadrilateral that satisfies the given conditions. Under each problem, explain what theorem(s) or definition(s) support your answer. Example: must be a rhombus Explanation of answer: A quadrilateral with all congruent sides is, by definition, a rhombus. (A square also has all congruent sides, but a square is a more specific type of rhombus. This quadrilateral does not HAVE to be a square to satisfy the conditions but it does HAVE to be a rhombus. A square is a type of rhombus.) 16. ; must be a 17. ; ; must be a

6 18. ; ; must be a 19., must be a (P is the intersection of the diagonals) 20. ; ; must be a 21. ; ; must be a 22. Show your work and find the missing variables in parallelogram ABDC. Find the values of all of the missing angles. What is the problem? (There is one!) A x B y E z 70 C w D 23. If = 8 6, = 3 + 4, = + 12, and = 7 + 7, find the value of x and y for which LMNO must be a parallelogram.

7 24. Draw a parallelogram ABCD and let the intersection of its diagonals be P. Answer the following questions and state the theorem(s) that you used. Each part is independent from another. a. If = 85, what is? Justify. b. If = 44, and = 46, what is? Justify. c. If = 3 + 3, = + 2, = 11, and = 5 6, find all 4 lengths. Justify. Note: You will need use a system of equations. d. If ABCD is a rhombus, = + 12, and = 5 3, find x. Justify. e. If ABCD is a rhombus, = 8, and = , find x. Justify.