Unit 6: Quadrilaterals

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Name: Period: Unit 6: Quadrilaterals Geometry Honors Homework Section 6.1: Classifying Quadrilaterals State whether each statement is true or false. Justify your response. 1. All squares are rectangles. 2. A rhombus can be a kite. 3. Every quadrilateral is a parallelogram. 4. A trapezoid is a parallelogram. 5. Some parallelograms are squares. 6. All rhombuses are squares. Name each type of special quadrilateral that can meet the given condition. Make sketches to support your answers. 7. Exactly one pair of congruent sides 8. Four right angles 9. Two pairs of parallel sides 10. Adjacent sides that are congruent State all possible names for each figure and then circle the most precise name for each figure. 17. 18. Find the value of the variables. Then find the lengths of the sides of each quadrilateral. 19. 20. 21. Find the measure of the variable and each angle. 22. 24. 25. 23.

Section 6.2: Properties of Parallelograms Find the value of x in each parallelogram. 1. 3. 5. 7. 2. 4. 6. 8. Find the measures of the numbered angles for each parallelogram. 9. 10. Find the length of TI in each parallelogram. 17. 18. 19. 20. If AE=17 and BF=18, find the measures of the sides of parallelogram BNXL. 21. BN 22. NX 23. XL 24. BL

Section 6.3: Proofs involving Parallelograms State whether the information given about quadrilateral SMTP is sufficient to prove that it is a parallelogram. 1. SPT SMT 2. SPX TMX, TPX SMX 3. SM PT, SP MT 4. SX XT, SM PT 5. PX MX, SX TX 6. SP MT, SP MT Find the values of x and y for which the figure must be a parallelogram. 7. 8. 9. Find the value of x. Then tell whether the figure must be a parallelogram. Explain your answer. 10. Decide whether the quadrilateral is a parallelogram. Explain your answer. 17. 19. 18. 20. Section 6.4: Special Parallelograms (rhombuses, rectangles, and squares) For each parallelogram choose the best name and find the measures of the numbered angles. 1. 2. 3. 5. 6. 4. HIJK is a rectangle. Find the value of x and the length of each diagonal. 7. HJ = x and IK = 2x 7 8. HJ = 3x + 5 and IK = 5x 9 9. HJ = 3x + 7 and IK = 6x 11 10. HJ = 19 + 2x and IK = 3x + 22

The parallelograms below are not drawn to scale. Can the parallelogram have the conditions marked? If not, write impossible. Explain your answer. For each rhombus find the measures of the numbered angles. Determine whether the quadrilateral can be a parallelogram. If not, write impossible. Explain your answer. 17. One pair of opposite sides is parallel and the other pair is congruent. 18. Opposite angles are congruent and supplementary, but the quadrilateral is not a rectangle. Do the following properties apply to rectangles, rhombi, and/or squares? List all that apply. 19. All sides are congruent. 20. Opposite sides are congruent. 21. Opposite sides are parallel. 22. Opposite angles are congruent. 23. All angles are right. 24. Consecutive angles are supplementary. 25. Diagonals bisect each other. 26. Diagonals are congruent. 27. Diagonals are perpendicular. 28. Each diagonal bisects opposite angles. Section 6.5: Trapezoids and Kites Find the measures of the numbered angles in each isosceles trapezoid. 1. 3. 5. 2. 4. Find the value of the variable(s) in each isosceles trapezoid. 6. 8. 7. 9.

Find the measures of the numbered angles in each kite. 10. Find the value of the variable(s) in each kite. 17. 18. Can two angles of a kite be as follows? Explain. 19. Opposite and acute 20. Consecutive and obtuse 21. Opposite and supplementary 22. Consecutive and supplementary 23. Opposite and complementary 24. Consecutive and complementary Unit 6 Review Find the correct word that completes each sentence. 1. A(n) is a parallelogram with four right angles. 2. A(n) is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent. 3. Angles of a polygon that share a common side are. 4. A(n) is a quadrilateral with exactly one pair of parallel sides. 5. A(n) is a parallelogram with four congruent sides. 6. The of a trapezoid is the segment that joins the midpoints of the nonparallel opposite sides. 7. A(n) is a quadrilateral with both pairs of opposite sides parallel. 8. A(n) is a parallelogram with four congruent sides and four right angles. 9. A(n) is a trapezoid whose nonparallel opposite sides are congruent. 10. Two angles that share a base of a trapezoid are its. Find the values of the variables and the lengths of the sides.

Find the measures of the numbered angles for each parallelogram. Determine whether the quadrilateral must be a parallelogram. 17. 18. 19. Find the values of the variables for which ABCD must be a parallelogram. 20. 22. 21. 23. Find the measures of the numbered angles in each quadrilateral. 24. 25. 26. Find AC for each quadrilateral. 27. 28. 29. 30. Does the information allow you to prove that ABCD is a parallelogram? Explain. 31. AC bisects BD 32. AB DC, AB DC 33. DAB BCD and ABC CDA 34. AB DC, BC AD Find the values of x and y in parallelogram ABCD. 35. AB = 2y, BC = y + 3, CD = 5x 1, DA = 2x + 4 36. AB = 2y + 1, BC = y + 1, CD = 7x 3, DA = 3x Determine whether each statement is always, sometimes or never true. 37. A rhombus is a square. 38. A square is a rectangle. 39. A rhombus is a rectangle. 40. The diagonals of a parallelogram are perpendicular. 41. The diagonals of a parallelogram are congruent. 42. Opposite angles of a parallelogram are congruent.

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