Question

show that of the diagonal of quad. bisect each other at right angle then it is a rhombus​

Answer 1

Answer:

Given - all diagonals are equal , all angle produced by diagonals are also equal. centre is o.

proove - quadrilateral (abcd) is a rhombus.

proof :-

★at first make a quadrilateral( we have to proove it a parallelogram )

★take 2 triangles opposite , one pair only

1. diagonal @ = diagonal $

2. angle 90° = 90°

3. diagonal € = diagonal £

so by SAS opposite triangles are congurent

★ by CPCT - 1. the border lines or AB and CD are equal . - eq1

★ by CPCT - 1. angles BAC = angle DCA ( alternate angles ) If they are alternate angles means the sides must be parallel

so AB // CD -eq2

By equation 1 and 2 -› AB =CD and AB//CD

If in a quaderilateral has one pair of opposite side equal and parallel then it is a parallelogram .

ABCD is a parallelogram

in a parallelogram all oposite ∆ triangles are equal .

★ take two unopposite ∆ triangles

∆ ABO and ∆ DAO

1. BO = DO ( CPCT )

2. angle AOB = angle DOA ( 90°)

3. AO common

By SAS -› ∆ ABO = ∆ DAO

★ By CPCT = AB = DA

AB = CD , BC = DA , AB = DA

then

AB = CD = BC = DA

In a parallelogram all sides are equal then it is rhombus .