1. **Problem Statement:** Given rectangle JKLM with vertices J (top-left), K (top-right), L (bottom-right), and M (bottom-left), and a diagonal JL drawn. (i) Name two triangles which are congruent. (ii) Prove the congruence of these triangles. 2. **Identifying the triangles:** The diagonal JL divides the rectangle into two triangles: \(\triangle JKL\) and \(\triangle JLM\). 3. **Properties of a rectangle:** - Opposite sides are equal and parallel. - All angles are right angles (90 degrees). - Diagonals are equal in length. 4. **Triangles to consider:** - \(\triangle JKL\) with vertices J, K, L. - \(\triangle JLM\) with vertices J, L, M. 5. **Proving congruence:** We will prove \(\triangle JKL \cong \triangle JLM\) using the Side-Angle-Side (SAS) criterion. 6. **Step-by-step proof:** - Side JL is common to both triangles. - Side JK is equal to side LM because opposite sides of a rectangle are equal. - Angle JKL and angle JLM are right angles (90 degrees) because all angles in a rectangle are right angles. 7. **Applying SAS criterion:** - Side JK = Side LM - Angle at K = Angle at M = 90 degrees - Side JL common Therefore, \(\triangle JKL \cong \triangle JLM\) by SAS congruence. **Final answer:** (i) The two congruent triangles are \(\triangle JKL\) and \(\triangle JLM\). (ii) They are congruent by SAS criterion: two sides and the included angle are equal.