1. WXYZ is a rectangle. If ZX = 6x – 4 and WY = 4x + 14, find ZX.
B. 36
C. 50
D. 54
5-Minute Check 1

2. WXYZ is a rectangle. If WY = 26 and WR = 3y + 4, find y.
B. 3
C. 4
D. 5
5-Minute Check 2

3. WXYZ is a rectangle. If mWXY = 6a2 – 6, find a.
B. ± 4
C. ± 3
D. ± 2
5-Minute Check 3

4. RSTU is a rectangle. Find mVRS.
B. 42
C. 52
D. 54
5-Minute Check 4

5. RSTU is a rectangle. Find mRVU.
B. 104
C. 76
D. 52
5-Minute Check 5

6. Given ABCD is a rectangle, what is the length of BC?
___
A. 3 units
B. 6 units
C. 7 units
D. 10 units
5-Minute Check 6

7. Recognize and apply the properties of rhombi and squares.
You determined whether quadrilaterals were parallelograms and/or rectangles.
Recognize and apply the properties of rhombi and squares.
Determine whether quadrilaterals are rectangles, rhombi, or squares.
Then/Now

8. rhombus
square
Vocabulary

9. Concept 1

10. Use Properties of a Rhombus
A. The diagonals of rhombus WXYZ intersect at V. If mWZX = 39.5, find mZYX.
Example 1A

11. Use Properties of a Rhombus
B. ALGEBRA The diagonals of rhombus WXYZ intersect at V. If WX = 8x – 5 and WZ = 6x + 3, find x.
Example 1B

12. A. ABCD is a rhombus. Find mCDB if mABC = 126.
A. mCDB = 126
B. mCDB = 63
C. mCDB = 54
D. mCDB = 27
Example 1A

13. B. ABCD is a rhombus. If BC = 4x – 5 and CD = 2x + 7, find x.
A. x = 1
B. x = 3
C. x = 4
D. x = 6
Example 1B

14. Concept 3

15. Concept

16. Is there enough information given to prove that ABCD is a rhombus?
Given: ABCD is a parallelogram. AD  DC
Prove: ADCD is a rhombus
Example 2

17. B. No, you need more information.
A. Yes, if one pair of consecutive sides of a parallelogram are congruent, the parallelogram is a rhombus.
B. No, you need more information.
Example 2

18. A. The diagonal bisects a pair of opposite angles.
Sachin has a shape he knows to be a parallelogram and all four sides are congruent. Which information does he need to know to determine whether it is also a square?
A. The diagonal bisects a pair of opposite angles.
B. The diagonals bisect each other.
C. The diagonals are perpendicular.
D. The diagonals are congruent.
Example 3

19. Understand Plot the vertices on a coordinate plane.
Classify Quadrilaterals Using Coordinate Geometry
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.
Understand Plot the vertices on a coordinate plane.
Example 4

20. Classify Quadrilaterals Using Coordinate Geometry
It appears from the graph that the parallelogram is a rhombus, rectangle, and a square.
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.
Example 4

21. Use slope to determine whether the diagonals are perpendicular.
Classify Quadrilaterals Using Coordinate Geometry
Use slope to determine whether the diagonals are perpendicular.
Example 4

22. Answer: ABCD is a rhombus, a rectangle, and a square.
Classify Quadrilaterals Using Coordinate Geometry
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.
Answer: ABCD is a rhombus, a rectangle, and a square.
Check You can verify ABCD is a square by using the Distance Formula to show that all four sides are congruent and by using the Slope Formula to show consecutive sides are perpendicular.
Example 4

23. C. rhombus, rectangle, and square
Determine whether parallelogram EFGH is a rhombus, a rectangle, or a square for E(0, –2), F(–3, 0), G(–1, 3), and H(2, 1). List all that apply.
A. rhombus only
B. rectangle only
C. rhombus, rectangle, and square
D. none of these
Example 4