Download App

Quadrilaterals — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsQuadrilaterals1 Mark
✓

Answer

  1. BC2 + AD2 + 2AB ⋅ CD
    Solution:

    Construction: Draw perpendicular from D and C on AB which meets AB at E and F, respectively.
    So, DEFC is a parallelogram, since one pair of opposite sides are parallel and equal.
    In $\triangle\text{ABC},$
    $\angle\text{B}$ is an acute angle.
    $\Rightarrow\text{AC}^2=\text{BC}^2+\text{AB}^2-2\text{AB}\times\text{AE}$
    In $\triangle\text{ABD},$
    $\angle\text{A}$ is an acute angle.
    $\Rightarrow\text{BD}^2=\text{AD}^2+\text{AB}^2-2\text{AB}\times\text{AF}$
    $\Rightarrow\text{AC}^2+\text{BD}^2=\text{BC}^2+\text{AD}^2+2\text{AB}(\text{AB}-\text{BE}-\text{AF})$
    $=\text{BC}^2+\text{AD}^2+2\text{AB}\times\text{EF}$
    $=\text{BC}^2+\text{AD}^2+2\text{AB}\times\text{CD}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q" from Quadrilaterals→Quadrilaterals — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

When $0 . \overline{001}$ is expressed in the form p/q, where p and q are integers not having any common factor except 1 then q is equal
→

How many linear equations are satisfied by x = 2 and y = -3?

  1. Only one.
  2. Two.
  3. Three.
  4. Infinitely many.
→
In $\triangle\text{ABC, }\text{BD}\perp\text{AC, }\angle\text{CAE} = 30^\circ$ and $\angle\text{CBD}=40^\circ.$ Then $\angle\text{AEB}=?$
→
The ratio between the radius of the base and the height of a cylinder is 2 : 3. If its volume is 1617cm3 then its total surface area is:
→
Write the correct answer in the following:
If $\frac{\text{x}}{\text{y}}+\frac{\text{y}}{\text{x}}=-1 \ (\text{x},\text{y}\neq0),$ the value of $\text{x}^3-\text{y}^3$ is.
→
The factors of 8a3 + b3 - 6ab + 1 are:
→
Is quadrilateral ABCD a rhombus?
  1. Quadrilateral ABCD is a || gm.
  2. Diagonals AC and BD are perpendicular to each other.
  1. If the question can be answered by one of the given statements alone and not by the other;
  2. If the question can be answered by either statement alone;
  3. If the question can be answered by both the statements together but not by any one of the two;
  4. If the question cannot be answered by using both the statements together.
→
If (k, -3) lies on the line 3x - y = 6, then the value of ‘k’ is:
→
If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:
→
A point both of whose coordinates are negative lies in quadrant.
→