Right-angled triangles ABC and ABD have a common hypothesis AB. It is known that BA is the bisector of the angle CBD
| February 19, 2021 | education
Right-angled triangles ABC and ABD have a common hypothesis AB. It is known that BA is the bisector of the angle CBD. Prove that AB is the bisector of the CAD angle.
Let us prove that right-angled triangles ABC and AВD are equal.
In right-angled triangles ABC and AВD, the hypotenuse AB is common, angle ABC = AВD since AB is the bisector of the angle СВD, then the right-angled triangles ABC and AВD are equal in hypotenuse and acute angle.
Then the angle СAВ = DAВ, which means AB is the bisector of the angle СAD, which was required to be proved.
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