Julius needs to determine how much information needs to be given about an isosceles triangle to be able to draw an isosceles triangle. He is looking at six different cases and is trying to determine if that amount of detail will allow him to construct just one isosceles triangle or if it allows for more than one isosceles triangle.

Case 1. The length of the two congruent sides and the measure of the included angle.

Case 2. The lengths of two non-congruent sides and the measure of the included angle.

Case 3. The lengths of two non-congruent sides.

Case 4. The measure of the two congruent angles and the included side.

Case 5. The measure of two non-congruent angles.

Case 6. The measure of two non-congruent angles and the included side.

Forms only one isosceles triangle: Forms more than one isosceles triangle: