Question

In the ∆ABC , ∟BAC=900 and AD┴BC, then correct statement from the following is. *

A. BD.CD=BC2
B. BD.CD=AD2
C. AB.AC=AC2
D. AB.AC=AD2
please help me​

Answer 1

$\huge \bold {BD.CD=AD2}$

Step by Step

In Triangle ABC, angle BAC = 90 degree and AD is perpendicular to BC

Given in the question a perpendicular is drawn AD on BC from angle BAC which is 90 degree

So, these two triangles ABD and CAD are similar

$\Delta \mathrm{ABD} \approx \Delta \mathrm{CAD}$

By Corresponding part of Similar Triangles (CPST),

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

This proves that the ratio of areas of two similar triangles is proportional to the squares of the corresponding sides of both the triangles.

$\text {we can write } \frac{B D}{A D}=\frac{A D}{C D}$

By cross-multiplication we get,

$\mathrm{BD} \times \mathrm{CD}=\mathrm{AD} \times \mathrm{AD}=\mathrm{AD}^{2}$

$\mathrm{BD} \times \mathrm{CD}=\mathrm{AD}^{2}$

Which is our Required Expression

Hence , option 2 is correct

Answer 2

Answer:

OPTION B

Step-by-step explanation:

YOU CAN SEE THE ANSWER ABOVE