Question

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can the smaller triangle be the image of the larger triangle under a dilation? (image shows two triangles with lines and points labeled)

Explanation:

Step1: Identify Similar Triangles

Check if the triangles have corresponding angles equal (AA similarity) or sides in proportion (SSS/SAS similarity). The smaller triangle (with vertices like \(a\), \(b\), \(c\)) and the larger triangle (with \(a'\), \(b'\), \(c'\)) share the same angles due to parallel lines or common angles, indicating similarity.

Step2: Verify Scale Factor

The sides of the larger triangle are scaled versions of the smaller one. For example, the distance from \(b\) to \(b'\), \(a\) to \(a'\), and \(c\) to \(c'\) are proportional, confirming similarity by SSS (if sides are proportional) or AA (if angles match).

Answer:

The two triangles (the smaller one and the larger blue one) are similar by the AA (Angle - Angle) or SSS (Side - Side - Side) similarity criterion, as they have corresponding angles equal and sides in proportion.