In the diagram below, AC and DG are parallel lines. B lies on AC, E and F lie on DG and triangle BEF is isosceles.
Prove that angle EBF is . Give reasons for each stage of your working.
Mark on the diagram that triangle BEF is isosceles.
AC and DG are parallel lines, so using alternate angles we know that angle BEF = . Mark this on the diagram.
Write the fact, and the reason using the key mathematical vocabulary
angle BEF = , alternate angles
Now using the fact that triangle BEF is isosceles, we can see that angle BFE = . Mark this on the diagram.
Write the fact, and the reason using the key mathematical vocabulary
angle BFE = , isosceles triangle
Now we can see that angle EBF is the last remaining angle in a triangle, and as the angles in a triangle sum to 180, angle EBF =
Write the fact, and the reason using the key mathematical vocabulary
angle EBF = , angles in a triangle sum to 180