Advertisements
Advertisements
Question
Show that each diagonal of a rhombus bisects the angle through which it passes.
Advertisements
Solution
\[\text{ In ∆ AED and ∆ DEC }: \]
\[ AE = EC (\text{ diagonals bisect each other })\]
\[AD = DC (\text{ sides are equal })\]
\[DE = DE (\text{ common })\]
\[\text{ By SSS congruence }: \]
\[ ∆ AED \cong ∆ CED\]
\[\angle ADE = \angle CDE (\text{ c . p . c . t })\]
\[\text{ Similarly, we can prove ∆ AEB and ∆ BEC, ∆ BEC and ∆ DEC, ∆ AED and ∆ AEB are congruent to each other } . \]
\[\text{ Hence, diagonal of a rhombus bisects the angle through which it passes } . \]
\[\]
RELATED QUESTIONS
The following figure is parallelogram. Find the degree values of the unknowns x, y, z.
In the following figure GUNS and RUNS are parallelogram. Find x and y.
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
Which of the following statement is true for a rhombus?
Its diagonals bisect each other at right angles.
Fill in the blank, inthe following, so as to make the statement true:
A square is a rhombus in which .....
Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.
In rhombus ABCD;
(i) if ∠A = 74° ; find ∠B and ∠C.
(ii) if AD = 7.5 cm ; find BC and CD.
If the adjacent sides of a parallelogram are equal then parallelogram is a ______.
If all sides of a quadrilateral are equal, it is a ______.
All rhombuses are squares.
