Question

1. based on the markings on the drawings, which triangles can not be proved congruent?

Explanation:

Step1: Analyze Option A

In figure A, we have two triangles with two sides marked equal (the tick marks) and the included side (the diagonal) common. By SSS (Side - Side - Side) or SAS (Side - Angle - Side, since the included angle between the equal sides is common), the triangles can be proven congruent.

Step2: Analyze Option B

In figure B, we have vertical angles (which are equal) and two sides marked equal (the tick marks). So by SAS (since we have two sides and the included angle - the vertical angle) or SSS (if we consider the vertical angles and the marked sides), the triangles can be proven congruent.

Step3: Analyze Option C

In figure C, we have two right - angled triangles with one leg marked equal (the tick marks) and the hypotenuse (the common side) and the right angle. By HL (Hypotenuse - Leg) theorem for right - angled triangles, or by SAS (right angle, one leg, and the hypotenuse can be related to sides), the triangles can be proven congruent.

Step4: Analyze Option D

In figure D, we have two triangles with one angle marked equal (the angle at the top) and one side marked equal (the side with the arrow). But we don't have enough information (like another side or angle) to prove congruence. The marked angle is not the included angle between the marked side and another side, and we don't have SSS, SAS, ASA, AAS or HL conditions met.

Answer:

D. The triangles in figure D