abc is a triangle in Which ab=ac and d is any point in bc prove that ab square -ad square = bd ×cd
Answers
Step-by-step explanation:
from the given info,
from the given info,In triangles BCD and ACB,
from the given info,In triangles BCD and ACB,BC/CD=AC/BC
from the given info,In triangles BCD and ACB,BC/CD=AC/BCNow, Angle BCD=angle ACB (Common Angle)
from the given info,In triangles BCD and ACB,BC/CD=AC/BCNow, Angle BCD=angle ACB (Common Angle)Hence, the two triangles are similar by SAS rule.
from the given info,In triangles BCD and ACB,BC/CD=AC/BCNow, Angle BCD=angle ACB (Common Angle)Hence, the two triangles are similar by SAS rule.So, angle DBC= angle DCB (as they are corresponding angles of similar triangles)
from the given info,In triangles BCD and ACB,BC/CD=AC/BCNow, Angle BCD=angle ACB (Common Angle)Hence, the two triangles are similar by SAS rule.So, angle DBC= angle DCB (as they are corresponding angles of similar triangles)i.e. angle DBC=angle ACB (as ACB and DCB are one and the same angle)
from the given info,In triangles BCD and ACB,BC/CD=AC/BCNow, Angle BCD=angle ACB (Common Angle)Hence, the two triangles are similar by SAS rule.So, angle DBC= angle DCB (as they are corresponding angles of similar triangles)i.e. angle DBC=angle ACB (as ACB and DCB are one and the same angle)At last, for triangle DBC,
from the given info,In triangles BCD and ACB,BC/CD=AC/BCNow, Angle BCD=angle ACB (Common Angle)Hence, the two triangles are similar by SAS rule.So, angle DBC= angle DCB (as they are corresponding angles of similar triangles)i.e. angle DBC=angle ACB (as ACB and DCB are one and the same angle)At last, for triangle DBC,DB=BC (as sides opp equal angles are equal