Question

Determine whether ASTU is similar to ASDC. If so state how do you know.

Answer 1

Similarity

Two similar triangles have the same angles in all cases. Let's compare angle by angle of both triangles and find if they are equal or not.

When two lines are crossed, the opposite angles are equal, they are called vertical angles:

In this case:

the red angles are equal. This is:

∠CSD = ∠TSU

For the rest of the angles....

we have that the triangle ΔSDC has a 63º angle,

and the triangle ΔSTU has not a 63º angle just a 66º angle and a 40º angle.

Then, ΔSDC and ΔSTU have not the same angles.

Then, they are not similar

Answer: D ΔSDC and ΔSTU are not similar