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Lesson 5 Menu

In the figure, WXYZ is a rectangle. Find ZX , if ZX = 6 x – 4 and WY = 4 x + 14. 2. In the figure, WXYZ is a rectangle. Find y , if WY = 26 and WR = 3 y + 4. 3. In the figure, WXYZ is a rectangle. Find a , if m  WXY = 6 a 2 – 6.

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Lesson 5 Menu

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  1. In the figure, WXYZ is a rectangle. Find ZX, if ZX = 6x – 4 and WY = 4x + 14. 2. In the figure, WXYZ is a rectangle. Find y, if WY = 26 and WR = 3y + 4. 3. In the figure, WXYZ is a rectangle. Find a, if mWXY = 6a2 – 6. • In the figure, RSTU is a rectangle. Find mVRS. • In the figure, RSTU is a rectangle. Find mRVU. Lesson 5 Menu

  2. Recognize and apply the properties of rhombi. • Recognize and apply the properties of squares. • rhombus • square Lesson 5 MI/Vocab

  3. Standard 7.0 Students prove and use theorems involvingthe properties of parallel lines cut by a transversal, the properties of quadrilaterals,and the properties of circles. (Key) Lesson 5 CA

  4. Lesson 5 TH1

  5. Given:BCDE is a rhombus, and Prove: ΔABEΔCDE Proof of Theorem 6.15 Lesson 5 Ex1

  6. Therefore, ΔABEΔCDE by SAS. Proof of Theorem 6.15 Lesson 5 Ex1

  7. Complete the following proof. Given:ACDF is a rhombus; Prove: ΔABGΔDEG Lesson 5 CYP1

  8. Statements Reasons 1. 1. Given 2. 2. Vertical Angles Theorem 3. 3. Diagonals of a rhombus bisect each other. 4. 4. Alternate Interior Angles Theorem 5. __________________ 5. ΔABGΔDEG ? Lesson 5 CYP1

  9. A. SSS B. SAS C. ASA D. AAS • A • B • C • D Lesson 5 CYP1

  10. Measures of a Rhombus A. Use rhombus LMNP to find the value of y if m1 = y2 – 54. Lesson 5 Ex2

  11. Measures of a Rhombus The diagonals of a rhombus are perpendicular. Substitution Add 54 to each side. Take the square root of each side. Answer: The value of y can be 12 or –12. Lesson 5 Ex2

  12. Measures of a Rhombus B. Use rhombus LMNP to find mPNL if mMLP = 64. Lesson 5 Ex2

  13. The diagonals of a rhombus bisect the angles. So, mPNL Measures of a Rhombus Opposite angles are congruent. Substitution Answer: 32 Lesson 5 Ex2

  14. A. Use rhombus ABCD and the given information to find the value of each variable.Find x if m1 = 2x2 – 38. • A • B • C • D A.x = 8 B.x = 4 or 12 C.x = 16 or –2 D.x = 8 or –8 Lesson 5 CYP2

  15. B. Use rhombus ABCD and the given information to find the value of each variable.Find mCDB if mABC = 126. • A • B • C • D A.mCDB = 126 B.mCDB = 63 C.mCDB = 54 D.mCDB = 27 Lesson 5 CYP2

  16. Squares 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. Explain. ExplorePlot the vertices on a coordinate plane. Lesson 5 Ex3

  17. Squares Plan If the diagonals are perpendicular, then ABCD is either a rhombus or a square. The diagonals of a rectangle are congruent. If the diagonals are congruent and perpendicular, then ABCD is a square. Solve Use the Distance Formula to compare the lengths of the diagonals. Lesson 5 Ex3

  18. Since the slope of is the negative reciprocal of the slope of the diagonals are perpendicular. The lengths of and are the same so the diagonals are congruent. ABCD is a rhombus, a rectangle, and a square. Squares Use slope to determine whether the diagonals are perpendicular. Lesson 5 Ex3

  19. Squares Examine The diagonals are congruent and perpendicular so ABCD must be a square. A square is also a rhombus. Answer: ABCD is a rhombus, a rectangle, and a square. Lesson 5 Ex3

  20. Diagonals of a Square CONSTRUCTION A square table has four legs that are 2 feet apart. The table is placed over an umbrella stand so that the hole in the center of the table lines up with the hole in the stand. How far away from a leg is the center of the hole? Let ABCD be the square formed by the legs of the table. Since a square is a parallelogram, the diagonals bisect each other. Since the umbrella stand is placed so that its hole lines up with the hole in the table, the center of the umbrella pole is at point E, the point where the diagonals intersect. Use the Pythagorean Theorem to find the length of a diagonal. Lesson 5 Ex4

  21. The distance from the center of the pole to a leg is equal to the length of Diagonals of a Square Lesson 5 Ex4

  22. Diagonals of a Square Answer: The center of the pole is about 1.4 feet from a leg of a table. Lesson 5 Ex4

  23. Lesson 5 CS1

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