25. Prove that in a right angled triangle square of the hypotenuse is

1.	25. Prove that in a right angled triangle square of the hypotenuse is equal to sum of the squaresofother two sides
Answer» construct a right triangle right angled at B. construction:construct a perpendicular BD on side AC. GIVEN:angleB=90 TO PROVE:AB^2+BC^2=AC^2 PROOF: In triangle ABD and triangle ABC, angle A=angle A angle ADB=angle BDC=90° therefore, triangle ADB is similar to triangle ABC. =>AD/AB=AB/AC (sides are in proportion) =>AD×AC=AB^2-------1 Similarly, triangle BDC is similar to triangle ABC BC/DC=AB/BC (sides are in proportion) which implies AC×DC=BC^2-----2 adding 1 and 2 AD.AC=AB^2 AD.AC+AC.DC=AB^2+BC^2 =AC(AD+DC)=AB^2+BC^2 =AC^2=AB^2+BC² Hence proved.

25. Prove that in a right angled triangle square of the hypotenuse is equal to sum of the squaresofother two sides

Answer»

construct a right triangle right angled at B.

construction:construct a perpendicular BD on side AC.

GIVEN:angleB=90

TO PROVE:AB^2+BC^2=AC^2

PROOF: In triangle ABD and triangle ABC,

angle A=angle A

angle ADB=angle BDC=90°

therefore, triangle ADB is similar to triangle ABC.

=>AD/AB=AB/AC (sides are in proportion)

=>AD×AC=AB^2-------1

Similarly, triangle BDC is similar to triangle ABC

BC/DC=AB/BC (sides are in proportion)

which implies AC×DC=BC^2-----2

adding 1 and 2

AD.AC=AB^2

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

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

=AC^2=AB^2+BC²

Hence proved.