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In order to prove 'Opposite angles of a ...

In order to prove 'Opposite angles of a cyclic quadrilateral are supplementary .'
(1) Draw a neat labelled figure.
(2) Write 'Given ' and 'To prove' from the figure drawn by you.

A

supplementary

B

complementary

C

equal

D

none of these

Text Solution

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The correct Answer is:
A
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Procedure : (i) Draw a circle of many radius with centre O. (ii) Mark any four points A,B,C and D on the boundary. Make a cyclic quadrilateral ABCD and name the angles as in Fig. 1 (iii) Make a replica of the cyclic quadrilateral ABCD with the help of tracing paper (iv) Make the cutout of the angles A,B,C and D as in Fig. 2 (v) Paste the angle cutout angle1,angle2,angle3 and angle4 adjacent to the angles opposite to A,B,C and D as in Fig . 3 Measure the angles angle1+angle3 , and angle2+angle4 . Observe the Fig. 3 and complete the following : {:((i),angleA+angleC= . . . . . . . ,(ii),angleB+angleD =. . . . . . .),((iii),angleC+angleA= . . . . . . .,(iv),angleD+angleB= . . . . . . .):} 2. Sum of opposite angles of a cyclic quadrilateral is . . . . . . . . 3. The opposite angles of a cyclic quadrilateral is . . . . . . .

In the adjacent figure BE bot DA and CD bot DA then prove that m angle1 ~= m angle3 .

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FULL MARKS-GEOMETRY-Additional Questions I. Multiple Choice Question.
  1. The angle sum of a convex polygon with number of sides 7 is . . . . ....

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  2. What is a regular polygon? State the name of a regular polygon of 3...

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  3. One angle of a parallelogram is a right. The name of the quadrilateral...

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  4. If all the four sides of a parallelogram are equal and the adjacent an...

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  5. In a parallelogram angleA:angleB=1:2. Then angleA . . . . . . . . .

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  6. Which of the following is a formula to find the sum of interior angles...

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  7. Diagonal of which of the following quadrilaterals do not bisect it two...

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  8. The point of concurrence of medians of a triangle is called centroid.

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  9. Orthocentre of a triangle is the point of concurrency of . . . . .. ....

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  10. ABCD is a parallelogram as shown. Find x and y.

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  11. A circle divides the plane into . . . . . . .part.

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  12. The longest chord of a circle is a . . . . . . . . . Of the circle.

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  13. In order to prove 'Opposite angles of a cyclic quadrilateral are suppl...

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  14. The value of x from figure is . . . . . . . . . If 'O' is the centre...

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  15. If PQ = x and 'O' is the centre of the circle, then x = . . . . . . ....

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  16. In figure OM=ON = 8cm and AB = 30 cm, then CD = . . . . . . . . .

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  17. O is the centre of a circle, angleAOB=100^(@). Then angle angleACB = ....

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  18. In,a circle, with center O, angleAOB=20^(@),angleBOC=40^(@), arc BC = ...

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  19. In the figure, OC=3 cm and radius of circle is 5 cm Then AB = . . ....

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  20. O is the centre of the circle. The value of x in the given diagram is ...

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