Question

In Δ ABC, angle ACB =90°
Seg CD perpendicular seg AB
Seg DE perpendicular seg CB
Show that :CD²×AC = AD ×AB ×DE

Answer 1

Answer:

Step-by-step explanation:

Answer:  

Given:  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.