(a) Prove that the sum of the angles in a triangle is 2 right angles.
(b) The side AB of a triangle ABC is produced to a point D. The bisector of ACB cuts AB at E. Prove that < CAE + < CBD = 2 < CEB.
Explanation
(a) Given any triangle ABC
To prove that < A + < B + < C = 180°
Construction: Produce BC to X and draw CP // BA.
Proof: with the lettering (a_{1} = a_{2}) (alternate angles);
(b_{1} = b_{2}) (corresponding angles)
(< BCA + < A + < B = 180° ; < ACB + < A + < B = 180°)
(therefore < A + < B + < C = 180°)
(b)
From the given triangle and with reference to letterings;
(hat{a} + hat{c} + hat{c} = hat{b}) (exterior opposite angles of a triangle)
(a + c = e) (exterior opposite angles of a triangle)
(a + b = a + a + c + c implies a + b = 2(a + c))
= (2e text{where e = a + c})
i.e (< CAE + < CBD = 2 < CED) (Proved)