Advertisements
Advertisements
प्रश्न
In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that \[∠COD = \frac{1}{2}(∠A + ∠B) .\]
Advertisements
उत्तर
\[ ∠COD = 180° - \left(∠OCD + ∠ODC \right)\]
\[ = 180°- \frac{1}{2}\left(∠C + ∠D \right)\]
\[ = 180°- \frac{1}{2}\left[ 360° - \left(∠A + ∠B \right) \right]\]
\[ = 180°- 180°+ \frac{1}{2}\left( ∠A + ∠B \right)\]
\[ = \frac{1}{2}\left( ∠A +∠B \right)\]
\[ = RHS\]
\[\text{ Hence proved } .\]
APPEARS IN
संबंधित प्रश्न
Complete of the following, so as to make a true statement:
A quadrilateral is convex if, for each side, the remaining ______ lie on the same side of the line containing the side.
In Fig. 16.19, ABCD is a quadrilateral.
How many pairs of opposite angles are there?
In the given figure, PQRS is an isosceles trapezium. Find x and y.
Complete the following statement by means of one of those given in brackets against each:
If in a quadrilateral only one pair of opposite sides are parallel, the quadrilateral is ................
Calculate the measure of each angle of a nonagon.
ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is ______.
What is the maximum number of obtuse angles that a quadrilateral can have?
The number of common points in the two angles marked in the following figure is ______.
Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them. Is the meeting point of the diagonals in the interior or exterior of the quadrilateral?
Investigate :
Use strips and fasteners to make a triangle and a quadrilateral.
Try to push inward at any one vertex of the triangle. Do the same to the quadrilateral. Is the triangle distorted? Is the quadrilateral distorted? Is the triangle rigid?
Why is it that structures like electric towers make use of triangular shapes and not quadrilaterals?
