Level 1: Core Concepts Check (Aiming for a Pass - 'S')

1. State the Theorem: What is the relationship between the exterior angle of a triangle and its interior opposite angles?

2. State the Theorem: What is the relationship between the sides and angles of an isosceles triangle?

3. Identify: If two angles of a triangle are equal, what can you say about the sides opposite those angles?

4. Calculate: In △PQR, the side QR is produced to S. If QP^R=70∘ and PQ^​R=60∘, find the exterior angle PR^S.

Level 2: Connecting the Dots (Aiming for a Credit - 'C'/'B')

1. Explain: The angles of a triangle are in the ratio 1:3:5. Find the size of each angle and determine what type of triangle it is.

2. Apply (Proof): In △ABC, AB=AC. The angle bisector of BA^C meets the side BC at D. Prove that AD is perpendicular to BC.

3. Problem-Solve: In the figure, AB is parallel to DC. Find the values of x and y. (Figure would be provided showing a transversal intersecting the parallel lines, forming a triangle with given angles)

Level 3: Exam Challenge (Aiming for a Distinction - 'A')

Proof Analysis: In △ABC, the point D lies on the side AC such that AB=BD=DC. If BA^C=x, prove that AC^B=2x and that AB^C=90∘−2x​.