Lesson 6­5 Rhombi and Squares with answers.notebook
January 12, 2015
Questions/Main Ideas Lesson 6­5 Rhombi and Squares
rhombus ­ a parallelogram with all four sides congruent
Theorems
6.15
If a parallelogram is a rhombus, then its diagonals are perpendicular.
AC BD
6.16
If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.
DAC ≅ BAC ≅ DCA ≅ BCA
ABD ≅ CBD ≅ ADB ≅ CDB
Questions/Main Ideas Example 1
The diagonals of rhombus WXYZ intersect at V. Use the given information to find each measure or value.
a.
If m WZX = 39.5, find m ZYX
b. If WX = 8x ­ 5 and WZ = 6x + 3, find x.
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Lesson 6­5 Rhombi and Squares with answers.notebook
January 12, 2015
Questions/Main Ideas Example 2
Use rhombus LMNP and the given information to find each value.
a.
find y if m 1 = y2 ­ 54
b.
find m PNL if m MLP = 64
Questions/Main Ideas square ­ a quadrilateral that is both a rectangle and a rhombus (four congruent sides and four congruent angles)
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Lesson 6­5 Rhombi and Squares with answers.notebook
January 12, 2015
Questions/Main Ideas Conditions for Rhombi and Squares
Theorem 6.17 If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. (Converse of Theorem 6.15)
Theorem 6.18 If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus. (Converse of Theorem 6.16)
Theorem 6.19 If one pair of consecutive sides of a parallelogram are congruent, the parallelogram is a rhombus.
Theorem 6.20 If a quadrilateral is both a rectangle and a rhombus, then it is a square.
Questions/Main Ideas Example 3
Determine whether parallelogram ABCD is a rhombus, a rectangle, or a square for A(­2, ­1), B(­1, 3), C(3, 2), and D(2, ­2). List all that apply.
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Lesson 6­5 Rhombi and Squares with answers.notebook
January 12, 2015
Questions/Main Ideas Example 4
A square table has four legs that are two feet apart. The table is placed over an umbrella stand so that the whole in the center of the table lines up with the whole in the stand. How far away from the legs is the center of the whole.
Example 5
Hector is measuring the boundary of a new garden. He wants the garden to be square. He has set each of the corner stakes 6 feet apart. What does Hector need to know to make sure that the garden is square?
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Lesson 6­5 Rhombi and Squares with answers.notebook
January 12, 2015
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Lesson 6­5 Rhombi and Squares with answers.notebook
January 12, 2015
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