Math, asked by Anonymous, 11 months ago

Question : refer to the attachment ! (3rd)​

Attachments:

Answers

Answered by rishu6845
5

Answer:

plzz give me brainliest ans and plzzzz follow me

Attachments:
Answered by ShreyaSrivastava221
0

Step-by-step explanation:

Given, ABCD is a right angled triangle and AC is perpendicular to BD

(i) consider two triangles ACB and DAB

⇒ We have ∠ ABC = ∠ DBC

⇒ ∠ ACB = ∠ DAB

⇒ ∠ CAB = ∠ ADB

∴ they are similar and corresponding sides must be proportional

i.e, ∠ ADC = ∠ ADB

∴ AB2 = BC × CD

(ii) ∠ BDA = ∠ BDC = 90°

⇒ ∠ 3 = ∠ 2 = 90° ∠ 1

⇒ ∠ 2 + ∠ 4 = 90° ∠ 2

⇒ From AAA criterion of similarity we have in two triangles if the angles are equal, then sides opposite to the equal angles are in the same ratio (or proportional) and hence the triangles are similar

Their corresponding sides must be proportional

= BC × DC

(iii) In two triangles ADB and ABC we have

∠ ADC = ∠ ADB

⇒ ∠ DCA = ∠ DAB

⇒ ∠ DAC = ∠ DBA

⇒ ∠ DCA = ∠ DAB

⇒ Triangle ADB and ABC are similar and so their corresponding sides must be proportion.

=

=

=

⇒ AD2 = DB × DC

Hence proved

Similar questions