# Given: QRST is a parallelogram. Prove: QRST is a square.

Complete the proof below by choosing the reason for line number 2 and line number 6.

Reason

Statement

1. QRST is a parallelogram.

Given

2. QRST is a rectangle

3. is a right angle

Definition of a right angle.

4.

Definition of perpendicular.

5. QRST is a rhombus

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

6. QRST is a square

(Points : 2)

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle; If the diagonals bisect the opposite angles then the parallelogram is a square.

A rectangle has 4 right angles; A square has 4 right angles.

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle; If the diagonals of a parallelogram are perpendicular then it is a square.

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle; If a quadrilateral is both a rectangle and a rhombus, then it is a square.

2. Determine whether parallelogram JKLM with vertices J(-1, 1), K(4, 1), L(4, 6) and M(-1, 6) is a rhombus, square, rectangle or all three. (Points : 2)

rhombus

square

rectangle

rhombus, square and rectangle

3. Quadrilateral ABCD with vertices A(4, 3), B(4, -2), C(-4, -2) and D(-4, 3) is a rectangle, find the length of the diagonals. (Points : 2)

5

8

4. Quadrilateral QRST is a rectangle. RT = 5x + 1 and QS = 6x – 3. Find QS.

(Points : 2)

8

21

42

4

5. In rhombus ABCD, the measure of angle ABE equals 38o, find the measure of angle BAE.(Points : 2)

76°

104°

90°

52°

6. Determine whether parallelogram JKLM with vertices J(-7, -2), K(0, 4), L(9, 2) and M(2, -4) is a rhombus, square, rectangle or all three. (Points : 2)

rhombus

square

rectangle

rhombus, square and rectangle

7. The area of the rectangle is 6675 in2, find the value of x.

(Points : 2)

6586 in

89 in

44.5 in

75 in

8. The sides of square ABCD are extended by the sides of equal length to form square MWTH. If MA = 6 and the area of ABCD is 144 cm2, find the area of MWTH.

(Points : 2)

360 cm2

180 cm2

129600 cm2

288 cm2

9. Find the perimeter and area of rectangle ABCD.

(Points : 2)

P = 75 in; A = 406.25 in2

P = 42.5 in; A = 375 in2

P = 85 in; A = 375 in2

P = 90 in; A = 406.25 in2

10. If the perimeter of a square is 64 cm, find the area. (Points : 2)

32 cm2

48 cm2

64 cm2

256 cm2