Question

a carpenter is building fink roof trusses to create the roof frame on a house. does her truss design include similar triangles? explain how you know.

Explanation:

Step1: Recall similarity criterion

Two triangles are similar if their corresponding angles are equal.

Step2: Analyze angles in triangles

In the given truss design, consider pairs of triangles. For example, in the left - hand side and right - hand side sub - triangles formed. In the triangles on the left with angles \(40^{\circ},50^{\circ},90^{\circ}\) (since \(180-(40 + 50)=90\)) and the triangles on the right with angles \(40^{\circ},50^{\circ},90^{\circ}\), and also the central triangles with angles \(60^{\circ},60^{\circ},60^{\circ}\). The corresponding angles of these triangles are equal.

Step3: Determine similarity

Since the corresponding angles of the triangles in the truss design are equal, the triangles are similar.

Answer:

Yes, the truss design includes similar triangles because the corresponding angles of the triangles in the design are equal.