Question

1. consider the triangle shown. click on the triangles that can be mapped onto △abc by a sequence of translations, rotations, reflections, or dilations. select all that apply.

Explanation:

Step1: Recall congruence and similarity criteria

Two triangles are congruent if they can be mapped onto each other by translations, rotations, and reflections. Similar - triangles can be mapped onto each other using dilations in addition to translations, rotations, and reflections. We need to check angle - measures and side - lengths.

Step2: Analyze angle - measures in \(\triangle ABC\)

In \(\triangle ABC\), the angles are \(100^{\circ}\), \(32^{\circ}\), and \(48^{\circ}\) (since the sum of angles in a triangle is \(180^{\circ}\), \(180-(100 + 32)=48\)).

Step3: Check each option for angle - measure and side - length correspondence

For a triangle to be mapped onto \(\triangle ABC\) by translations, rotations, reflections, or dilations:

• Option 1: The top - left triangle has angles \(100^{\circ}\), \(48^{\circ}\), and \(32^{\circ}\) and side - lengths \(6.5\) cm, \(3.5\) cm. It can be mapped onto \(\triangle ABC\) by a sequence of translations, rotations, or reflections (it is congruent).
• Option 2: The top - middle triangle has angles \(100^{\circ}\), \(32^{\circ}\), and \(48^{\circ}\) and side - lengths \(6.5\) cm, \(3.5\) cm. It can be mapped onto \(\triangle ABC\) by a sequence of translations, rotations, or reflections (it is congruent).
• Option 3: The top - right triangle has angles \(100^{\circ}\), \(32^{\circ}\), and \(48^{\circ}\) and side - lengths \(6.5\) cm, \(3.5\) cm. It can be mapped onto \(\triangle ABC\) by a sequence of translations, rotations, or reflections (it is congruent).
• Option 4: The bottom - left triangle has angles \(122^{\circ}\), \(20^{\circ}\), and \(38^{\circ}\). Since the angle - measures do not match those of \(\triangle ABC\), it cannot be mapped onto \(\triangle ABC\) by translations, rotations, reflections, or dilations.
• Option 5: The bottom - middle triangle has angles \(122^{\circ}\), \(38^{\circ}\), and \(20^{\circ}\). Since the angle - measures do not match those of \(\triangle ABC\), it cannot be mapped onto \(\triangle ABC\) by translations, rotations, reflections, or dilations.
• Option 6: The bottom - right triangle has angles \(100^{\circ}\), \(32^{\circ}\), and \(48^{\circ}\) and side - lengths \(6.5\) cm, \(3.5\) cm. It can be mapped onto \(\triangle ABC\) by a sequence of translations, rotations, or reflections (it is congruent).

Answer:

The triangles that can be mapped onto \(\triangle ABC\) are the top - left, top - middle, top - right, and bottom - right triangles.