Question

А
17.
In ∆ABC, AD | BC and AD = BC x CD,
prove that AABC is a right angled triangle.
B
с
D
Contd..on 3rd page​

Answer 1

Answer:

GIVEN: In triangle ABC, AD is perpendicular to BC and

AD^=BD×DC

TO PROVE: BAC=90°

PROOF: In right triangle ADB and triangle ADC,

Pythagoras theorem should be applied,then

AB^=AD^+BD^----- equation 1

AC^=AD^+DC^----- equation 2

AB^+BC^=2AD^+BD^+DC^

= 2BD^×CD+BD^+CD^ (.: AD^=BD×CD)

= (BD+CD)^ =BC^

Thus, in triangle we have,AB^+AC^=BC^

Hence, triangle ABC is a right triangle right angled at A

<BAC=90°

HENCE PROVED...