Question

ÚABC ~= ÚACB
BD perpendicular AC
The sum fo the three angles in any triangle is 180 degree.

Prove: mÚCBD = 1/2 mÚBAC

Answer 1

angle ABC ~= angle ACB
BD perpendicular AC
The sum fo the three angles in any triangle is 180 degree.

Prove: mangle CBD = 1/2 mangle BAC

Answer 2

let angle CBD = a

in trianagle ABC:
2x + y = 180

in triangle BCD
a + x = 90 or 2a + 2x = 180

then 2a + 2x = 2x + y , both equal to 180
2a = y
a = (1/2y
or
angle CBD = (1/2) angle BAC