a)
The pair of similar triangles are triangles ABD and ACD
b)
The triangle is given such that angle A is 90°
If point D is on line BC, then it touches angle A. However line AD is perpendicular to line BC,which means it splits the angle at A into two equal halves.
Hence, you now have two right angled triangles, on the one hand, triangle ABD and on the other hand, triangle ACD. The first one has angle D measuring 90° and line AB as the hypotenuse. The second one also has angle D measuring 90° with it's hypotenuse at line AC.
c)
The angle A which is 90 degree has been splitted into two(2) equal halves by the line segment AD, thus each angle is 45 degrees.
This is shown in the diagram below:
Applying the Tangent trigonometry ratio to solve for the line segment DA, we have:
[tex]\begin{gathered} \text{Tan 45}^0=\frac{opposite}{adjacent} \\ \text{Tan 45=}\frac{9}{|DA|} \\ 1=\frac{9}{|DA|} \\ |DA|=9 \end{gathered}[/tex]
Hence, the length of the line segment DA is 9 units
