11.
In a right-angled triangle with sides a and b and
hypotenuse c, the altitude drawn on the hypotenuse
is x. Then which condition(s) are true.
Answers
Answer:
It is given that AB=a, BC=b, AC=c and BE=x.
Also, ABC is a right angled triangle, which is right angled at B and BE⊥AC.
From ΔABC and ΔAEB, we have
∠ABC=∠AEB=90°
∠BAC=∠EAB(Common)
Thus, By AA similarity,
ΔABC is similar to ΔAEB.
Therefore, using the similarity condition, we have
\frac{AC}{AB}=\frac{BC}{EB}
AB
AC
=
EB
BC
\frac{c}{a}=\frac{b}{x}
a
c
=
x
b
cx=abcx=ab
Hence, ab=cxab=cx , thus proved.
please mark me as brainiest answer
Answer:
It is given that AB=a, BC=b, AC=c and BE=x.
Also, ABC is a right angled triangle, which is right angled at B and BE⊥AC.
From ΔABC and ΔAEB, we have
∠ABC=∠AEB=90°
∠BAC=∠EAB(Common)
Thus, By AA similarity,
ΔABC is similar to ΔAEB.
Therefore, using the similarity condition, we have
\frac{AC}{AB}=\frac{BC}{EB}
AB
AC
=
EB
BC
\frac{c}{a}=\frac{b}{x}
a
c
=
x
b
cx=abcx=ab
Hence, ab=cxab=cx , thus prov
It is given that AB=a, BC=b, AC=c and BE=x.
Also, ABC is a right angled triangle, which is right angled at B and BE⊥AC.
From ΔABC and ΔAEB, we have
∠ABC=∠AEB=90°
∠BAC=∠EAB(Common)
Thus, By AA similarity,
ΔABC is similar to ΔAEB.
Therefore, using the similarity condition, we have
\frac{AC}{AB}=\frac{BC}{EB}
AB
AC
=
EB
BC
\frac{c}{a}=\frac{b}{x}
a
c
=
x
b
cx=abcx=ab
Hence, ab=cxab=cx , thus proved.