ORProve that n a rishi triangle, the square on the hapomm ise gw:amoit

1.	ORProve that n a rishi triangle, the square on the hapomm ise gw:amoitha
Answer» Given:triangle ABC is a right triangle right angled at B RTP: AC^2= AB^2+AC^2 CONSTRUCTION :Draw BD_\|_ AC Proof:triangle ADB~triangle ABC => AD÷AB=AB÷AC AC.AD=AB^2 ………….. (1) Also triangle BDC~triangle ABC CD÷BC=BC÷AC CD.AC=BC^2 ………….. (2) On adding (1) & (2) AD.AC+CD.AC=AB^2+BC^2 AC (AD+CD)=AB^2+BC^2 AC.AC=AB^2+BC^2 ∴AC²=AB²+BC²

ORProve that n a rishi triangle, the square on the hapomm ise gw:amoitha

Answer»

Given:triangle ABC is a right triangle right angled at B

RTP: AC^2= AB^2+AC^2

CONSTRUCTION :Draw BD_|_ AC

Proof:triangle ADB~triangle ABC

=> AD÷AB=AB÷AC

AC.AD=AB^2 ………….. (1)

Also triangle BDC~triangle ABC

CD÷BC=BC÷AC

CD.AC=BC^2 ………….. (2)

On adding (1) & (2)

AD.AC+CD.AC=AB^2+BC^2

AC (AD+CD)=AB^2+BC^2

AC.AC=AB^2+BC^2

∴AC²=AB²+BC²