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When proving that a quadrilateral is a parallelogram by using slopes, you must find:

When proving that a quadrilateral is a parallelogram by using slopes, you must find: Correct Answer the slopes of all four sides

Parallelogram is a quadrilateral where both pairs of opposite sides are parallel.

Properties of parallelograms:

  • Opposite sides are congruent (AB = DC)
  • Opposite angels are congruent (D = B)
  • Consecutive angles are supplementary (A + D = 180°)
  • If one angle is right angle, then all angles are right
  • The diagonals of a parallelogram bisect each other
  • Each diagonal of a parallelogram separates it into two congruent
When proving that a quadrilateral is a parallelogram by using slopes, you must find the slopes of all four sides. If the slopes of opposite sides are equal, then the quadrilateral is a parallelogram.

Related Questions

In the given figure, PQRS is a parallelogram, a length and a breadth of the parallelogram are 80 cm and 25 cm respectively. If h1 + h2 = 84 cm, where h1 & h2 are the perpendiculars on the length and breadth of the parallelogram, then find the area of the parallelogram.
The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. The area of the parallelogram with base 15 cm is what percentage of the area of rectangle with length 20 cm? I) The height of the parallelogram is 20% less than the breadth of the rectangle. II) The height of the parallelogram is 60% of the length of the rectangle. III) The area of the rectangle is 66.67% more than the area of the parallelogram.
S1: If you want to do well in your examinations you need to be able to think for yourself which means not just following the guide-books but write what you think yourself.
P: That will not help much.
Q: Few if any students do this.
R: By discussing things with other students, with your teachers, and with any intelligent people you meet you will find you can pick up a lot of new ideas but it is not good first accepting these ideas, swallowing them undigested and then repeating them in the examination.
S: At first you will find it difficult but if you go on trying you will find clear independent thought becomes easier.
S6: If however you turn these ideas over in our mind accepting those which you agree with and fitting them into your stock of knowledge and rejecting the others you may get somewhere.

The Proper sequence should be:
In the given figure, PQRS is a parallelogram in which ∠SPQ = 30° and area of the parallelogram is 76 cm2. If PQ ∶ PS is 9.5 ∶ 4, then find the ratio of numerical value of area and perimeter of the parallelogram.
In parallelogram PQRS, ∠P = 45°, PR and QS are the diagonals of the parallelogram. The mid-point QR is O. OX and OY are perpendicular to PQ and QR respectively. If OX = 8 cm and OY = 12 cm, then what is the area of the parallelogram PQRS?
In a parallelogram, two sides are of length 5 cm and 10 cm respectively while the ratio of two diagonals of the parallelogram is 1 : 3, then what is the difference between the length of both the diagonals of the parallelogram?
In a parallelogram the side of the parallelogram is 12 cm. While the length of adjacent side is 16.66% more than the length of its adjacent side. What is the sum of squares of diagonal of the parallelogram?
Read the passage carefully and select the best answer to each question out of the given four alternatives. One should consciously engage in activities that will nourish your soul. Just as we nourish the body, we need to nurture the soul to connect to the creative power ofthe universe and to manifest joy in our lives. Often, we forget to address the soul, lost as we are in a jungle of material and sensual pleasures. But the more youembrace what feeds your soul, the happier you become. So if you want to enjoy the abundance of life, engage in what enriches your soul. Nurturing the soul is allabout finding calm amidst chaos. There are a number of practices that empower people towards this end including silent contemplation, various forms of meditation,yoga and tai chi However, the rigor and discipline involved in the pursuit of such practices often seems to discourage people. Add to this, the temptations of thematerial world that leave little time and motivation for anyone to pursue the spiritual path. Poet Walt Whitman declared: “Whatever satisfies the soul is truth”. Thegood news is that simple, everyday activities can also nutrify the soul — like spending time in the midst of nature, dancing in the rain or just putting thoughts onpaper. Do whatever is calming and pleases you. Creative pursuits are particularly appealing as inside each one of us, there is an artist craving for release andawaiting an opportunity for expression. One of the ways to indulge the artist within is to get started with the practice of any one or more of the creative art formssuch as music, singing, dancing, acting, drawing, painting, sculpting, poetry, fiction or essay writing. When you engage in such soul nourishing activities, all thought and energy gets focused toward goal accomplishment. At this point, you will find that even unknownforces of the universe are conniving to assist you in your amateurish but sincere attempts. As you progress, you are motivated to do better. You touch and access afaculty, a part of you that you never knew existed. Your inner artist is unleashed, baring the beauty of your soul that has found a fond medium of expression. Forinstance, a sculptors soul is seen in his artwork; a musicians in his compositions; an actors in his acting, a painters in his paintings and so on. It is immaterialwhether your effort is an immaculate artwork or just a clumsy attempt by a layperson. The idea is to try, be inspired and to create giving free rein to the mind. AsMichelangelo remarked: “I saw the angel in the marble and carved until I set him free”! What can you infer from Michelangelos statement - "I saw the angel in the marble and carved until I set him free"?
Given steps in procedure to find the center of gravity of the quadrilateral ABCD. Arrange the steps. i. Draw lines joining G1 with G2 and G3 with G4. ii. In given quadrilateral draw diagonal BD and locate centers of gravity G1, G2 of triangles BCD and ABD. iii. The point of intersection of lines G1G2 and G3G4 gives the center of gravity of the quadrilateral ABCD. iv. Similarly draw the diagonal AC and determine the centers of gravity G3, G4 of triangles ABC and ADC.
Read the passage carefully and select the best answer to each question out of the given four alternatives. One should consciously engage in activities that will nourish your soul. Just as we nourish the body, we need to nurture the soul to connect to the creative power ofthe universe and to manifest joy in our lives. Often, we forget to address the soul, lost as we are in a jungle of material and sensual pleasures. But the more youembrace what feeds your soul, the happier you become. So if you want to enjoy the abundance of life, engage in what enriches your soul. Nurturing the soul is allabout finding calm amidst chaos. There are a number of practices that empower people towards this end including silent contemplation, various forms of meditation,yoga and tai chi However, the rigor and discipline involved in the pursuit of such practices often seems to discourage people. Add to this, the temptations of thematerial world that leave little time and motivation for anyone to pursue the spiritual path. Poet Walt Whitman declared: “Whatever satisfies the soul is truth”. Thegood news is that simple, everyday activities can also nutrify the soul — like spending time in the midst of nature, dancing in the rain or just putting thoughts onpaper. Do whatever is calming and pleases you. Creative pursuits are particularly appealing as inside each one of us, there is an artist craving for release andawaiting an opportunity for expression. One of the ways to indulge the artist within is to get started with the practice of any one or more of the creative art formssuch as music, singing, dancing, acting, drawing, painting, sculpting, poetry, fiction or essay writing. When you engage in such soul nourishing activities, all thought and energy gets focused toward goal accomplishment. At this point, you will find that even unknownforces of the universe are conniving to assist you in your amateurish but sincere attempts. As you progress, you are motivated to do better. You touch and access afaculty, a part of you that you never knew existed. Your inner artist is unleashed, baring the beauty of your soul that has found a fond medium of expression. Forinstance, a sculptors soul is seen in his artwork; a musicians in his compositions; an actors in his acting, a painters in his paintings and so on. It is immaterialwhether your effort is an immaculate artwork or just a clumsy attempt by a layperson. The idea is to try, be inspired and to create giving free rein to the mind. As Michelangelo remarked: “I saw the angel in the marble and carved until I set him free”! According to the passage, what makes us really happy?