Question

identify the two smaller triangles in the diagram, then sketch them so the corresponding sides and angles have the same orientation.
11.
12.

Explanation:

11.

Step1: Identify the two smaller triangles

In the triangle \( \triangle JKL\), since \( JM\perp LK\) and \( JK\perp LK\), the two smaller right - angled triangles are \( \triangle JML\) and \( \triangle JMK\).

Step2: Sketch the triangles

Sketch \( \triangle JML\) and \( \triangle JMK\) with the right - angles at \( M\) and \( K\) respectively. Ensure that the angles \( \angle JML=\angle JMK = 90^{\circ}\), \( \angle L\) is common to \( \triangle JML\) and \( \triangle JKL\), and \( \angle J\) is common to \( \triangle JMK\) and \( \triangle JKL\).

12.

Step1: Identify the two smaller triangles

In the triangle \( \triangle WYZ\), since \( WX\perp YZ\) and \( ZX\perp WY\), the two smaller right - angled triangles are \( \triangle WXZ\) and \( \triangle YXZ\).

Step2: Sketch the triangles

Sketch \( \triangle WXZ\) and \( \triangle YXZ\) with the right - angles at \( X\). Ensure that \( \angle WXZ=\angle YXZ = 90^{\circ}\), \( \angle W\) is common to \( \triangle WXZ\) and \( \triangle WYZ\), and \( \angle Y\) is common to \( \triangle YXZ\) and \( \triangle WYZ\).

Answer:

1. The two smaller triangles are \( \triangle JML\) and \( \triangle JMK\).
2. The two smaller triangles are \( \triangle WXZ\) and \( \triangle YXZ\).