Find the Measures of the Numbered Angles in Each Rhombus

Name

Class

Date

Review 6.4/ 6.5/ 6.7

Decide whether the parallelogram is a rhombus, a rectangle, or a

square. Explain.

1. 2. 3.

Find the measures of the numbered angles in each rhombus.

4. 5.

6. 7.

8.

Algebra HIJK is a rectangle. Find the value of x and the length of each diagonal.

9. HJ = x and IK = 2x -7 10. HJ = 3x + 5 and IK = 5x -9

Determine the most precise name for each quadrilateral.

11. 12.

For what value of x is the figure the given special parallelogram?

13. rhombus 14. rectangle

15. rectangle

Determine whether each statement is true or false. If it is false, rewrite the sentence to make it true. If it is true, list any other quadrilaterals for which the sentence would be true.

16. Rhombuses have four congruent sides.

17. Rectangles have four congruent angles.

18. The diagonals of a rectangle bisect the opposite angles.

19. The diagonals of a rhombus are always congruent.

20. What is the most precise name for quadrilateral ABCD with vertices A(-5, -4), B (-3, 0), C (3, 2), D(1, -2).

21.  What is the most precise name for quadrilateral QRST with vertices Q(-2, 1), R(0, 2), S(2, -2), and T(0, -3).

22.  Prove that parallelogram HAPY with vertices H(-5, 3), A(1, 3), P(1, -3), and Y(5, -3) is a rhombus by showing that it has perpendicular diagonals. (Hint: use slope formula)

23.  Use the distance formula to prove that that parallelogram BMOP with vertices B(3, 5), M(7,6), O(6, 2), and P(2, 1) has to be a square or a rhombus.

24.  In the coordinate plane, draw parallelogram QRST with vertices Q(-2, 1), R(0, 2), S(2, -2), and T(0, -3). Then use slope to prove that QRST is a rectangle.

You must know your definition of Rectangle, Square, and Rhombus!!!!!! What are the rules for each? How do you know if it’s a rectangle, square or rhombus??