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
#5 and 6 is a and d
8. 360cm^2
7. 75in
5. 52 degrees
For line number 2, the reason would be "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."
For line number 6, the reason would be "If a quadrilateral is both a rectangle and a rhombus, then it is a square."
By using these reasons, we can conclude that if QRST is a parallelogram, and the diagonals of QRST are congruent and bisect the opposite angles, then QRST is a square.
Nice assignment you have there.
You don't actually expect one of us to do it for you, do you?
Tell you what, you post your choices of answer and somebody will tell you if you are correct or not.