Question

question 6
are the two triangles abc and def shown in the figure similar?

Explanation:

Step1: Identify the figure type

The figure is a rectangle (since all angles are right angles, \( \angle A=\angle D = 90^\circ \), and opposite sides are equal and parallel). So, \( AB \parallel CD \) and \( AD \parallel BC \), and all angles are \( 90^\circ \).

Step2: Analyze angles of triangles

For \( \triangle ABC \) and \( \triangle DEF \):

• \( \angle A=\angle D = 90^\circ \) (right angles of the rectangle).
• \( \angle ABC \) and \( \angle DEF \): Since \( BC \parallel FE \) (as \( BC \) and \( FE \) are both parallel to \( AD \) or \( AB \) in the rectangle - like structure), the corresponding angles are equal (alternate interior angles or corresponding angles due to parallel lines). Similarly, \( \angle ACB=\angle DFE \).

Step3: Apply AA similarity criterion

The AA (Angle - Angle) similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. Here, \( \angle A=\angle D \) and \( \angle ABC=\angle DEF \) (or \( \angle ACB=\angle DFE \)), so by AA similarity, \( \triangle ABC \sim \triangle DEF \).

Answer:

Yes, the two triangles \( ABC \) and \( DEF \) are similar.