NAME
6 -5
DATE
PERIOD
Skills Practice Rhombi and Squares
ALGEBRA Quadrilateral DKLM is a rhombus. 1. If DK = 8, find KL. 8
D
K A
2. If m∠DML = 82 find m∠DKM. 41
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L
3. If m∠KAL = 2x – 8, find x. 49 4. If DA = 4x and AL = 5x – 3, find DL.
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5. If DA = 4x and AL = 5x – 3, find AD. 12 6. If DM = 5y + 2 and DK = 3y + 6, find KL. 12 3
4
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Statements
Reasons
1. RSTU is a parallelogram. −− −− −− −− RX TX SX UX 2. RX = TX = SX = UX 3. RX + XT = RT, SX + XU = SU 4. RX + XT = SU 5. RT = SU −− −− 6. RT SU 7. RSTU is a rectangle.
1. Given 2. 3. 4. 5. 6. 7.
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5
Definition of congruent segments Seg Add Postulate Substitution Property Transitive Property Definition of segment If diagonals , the figure is a rectangle.
COORDINATE GEOMETRY Given each set of vertices, determine whether QRST is a rhombus, a rectangle, or a square. List all that apply. Explain. 8. Q(3, 5), R(3, 1), S(-1, 1), T(-1, 5)
Rhombus, rectangle, square; all sides are congruent and the diagonals are perpendicular and congruent. 9. Q(-5, 12), R(5, 12), S(-1, 4), T(-11, 4)
Rhombus; all sides are congruent and the diagonals are perpendicular, but not congruent. 10. Q(-6, -1), R(4, -6), S(2, 5), T(-8, 10)
Rhombus; all sides are congruent and the diagonals are perpendicular, but not congruent. 11. Q(2, -4), R(-6, -8), S(-10, 2), T(-2, 6)
None; opposite sides are congruent, but the diagonals are neither congruent nor perpendicular. Chapter 6
33
Glencoe Geometry
Lesson 6-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7. PROOF Write a two-column proof. Given: RSTU is a parallelogram. −−− −− −− −−− RX TX SX UX Prove: RSTU is a rectangle. Proof
