Question

In ∆ABC, <ACB = 90°,<CDB=90°,<DEB=90°,
Show that CD2 x AC = AD X AB XDE
on​.

Answer 1

Step-by-step explanation:

ABC is a right triangle,

In which

Also, and  

Where D is any point in AB and E is any point in CB.

To prove :

Proof:

In triangles, ACB and ADC,

 ( Reflexive)

  ( Right angles)

Thus, By AA similarity postulate,

-------(1)

⇒

⇒ -----------(2)

Now, Similarly,

 ----------(3)

Now, In triangles CED and CDB,

 ( Reflexive)

  ( Right angles)

By AA similarity postulate,

----------(4)

By equation (3) and (4),

-------(5)

Again by equation (1) and (5)

------------(6)

Multiplying equation (2) by on both sides,

From equation (6),

Hence Proved.

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