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August 1, 2014

Homework Help: geometry

Posted by karrie on Thursday, January 5, 2012 at 12:03pm.

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

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