Below is a proof which needs an auxiliary line. Introduce segment Paragraph form of proof. Introduce AD by the line postulate. Sometimes you are asked to prove segments or angles congruent but the triangles they are in that can be proven congruent overlap each other as below. Triangles are classified by side or by angles.
Scalene triangles have no congruent sides.
Isosceles triangles have at least two congruent sides. If two sides of a triangle are not congruent then the bigger angle is opposite the bigger side BSBA - If two angles of a triangle are not congruent then the bigger side is opposite the bigger angle. If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of a 2nd right triangle then the triangles are congruent. Classify the triangle in question 1 by its sides. Prove each of the following.