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Draw a rough figure, of a quadrilateral ...

Draw a rough figure, of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.

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Determine the truth value of the following statement. A quadrilateral is a parallelogram if and only if its opposite sides are parallel.

Can a quadrilateral ABCD be a parallelogram, if angleD + angleB = 180^@ ?

We know that parallelogram is also a quadrilateral. Let us also split such a quadrilateral into two triangles, find their areas ad hence that of the parallelogram . Does this agree with the formula that you know already?

The measures of two adjacent angles of a parallelogram are in the ratio 3:2 . Find the measure of each of the angles of the parallelogram.

Prove that the bisectors of the opposite angles of a parallelogram are parallel.

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

Find the truth values of the followings: (iii) (tit) For all parallelograms, opposite sides are equal

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle.

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the bisectors of the corresponding angles of the triangles. [The end-points of the angular bisectors are on the opposite sides of the angles.]

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ASHOK PUBLICATION ASSAM-Understanding Quadrilaterals.-EXAMPLE
  1. Explain how a square is. a parallelogram

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  2. Explain how a square is. a rhombus

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  3. Explain how a square is. a rectangle

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  4. Name the quadrilaterals whose diagonals. bisect each other

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  5. Name the quadrilaterals whose diagonals. are perpendicular bisectors...

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  6. Name the quadrilaterals whose diagonals. are equal

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  7. Explain why a rectangle is a convex quadrilateral.

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  8. ABC is a right-angled triangle and O is the mid point of the side oppo...

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  9. Take any quadrilateral, say ABCD , Divide it into two triangles, by dr...

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  10. Take four congruent card-board copies of any quadrilateral ABCD, with ...

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  11. Take four congruent card-board copies of any quadrilateral ABCD, with ...

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  12. Consider a concave quadrilateral ABCD, Split it into two triangles and...

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  13. Take a regular hexagon. What is the sum of the measures of its exter...

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  14. Take a regular hexagon. Is x=y=z=p=q=r where x,y,z,p,q,r are exterio...

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  15. What is the measure of each exterior angle?

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  16. What is the measure of each interior angle?

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  17. Draw a rough figure, of a quadrilateral that is not a parallelogram bu...

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  18. A mason has made a concrete slab. He needs it to be rectangular. In wh...

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  19. A square was defined as a rectangle with all sides equal. Can we defin...

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  20. Can a trapezium have all angles equal? Can it have all sides equal? Ex...

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