Question

Prove that quadrilateral ABCD is a square, using Pythagorean Therom.

How to find the formula for the Pythagorean therom c2=a2+b2

The quadrilateral is in the picture above..

Answer 1

Break into two parts

• ∆ABC and ∆ADC

In∆ABC

`\\ \sf\longmapsto AC^2=9^2+9^2=81+81=162\implies AC=9√2`

In ∆ADC

`\\ \sf\longmapsto AC^2=9^2+9^2=81+81=162\implies AC=9√2`

• <D=<B=90°

ABCD is a square.

Answer 2

• See below

Explanation:

The given diagram doesn't give enough details to state the quadrilateral is a square.

We see all sides are of same length of 9 units. This could be a rhombus too.

In order this quadrilateral is a square all interior angles should be marked as right angles.

Let's assume the above condition is met.

Find the length of both diagonals:

• 
  `AC=√(9^2+9^2) =9√(2) \\BD=√(9^2+9^2) =9√(2)`

Since both diagonals have same length, the quadrilateral is a square.