Question

19/20 geometry a reflections the image of △abc after a reflection across de is △abc. which triangle must be a right triangle and why? △abc is right because it is the image of △abc. △bcg is right because b lies on the line of reflection. △adc is right because a lies on ad.

Explanation:

Step1: Recall reflection property

A reflection is a rigid - motion. Rigid motions preserve shape and size, including angle measures. A right - triangle has one angle equal to 90 degrees. When a triangle is reflected, the angle measures of the original triangle and its image are the same.

Step2: Analyze each option

• Option 1: There is no information given about $\triangle ADC$ being right and its relation to the reflection of $\triangle ABC$.
• Option 2: $\triangle BCG'$ is not the image of $\triangle ABC$ and there is no indication it is right based on the reflection of $\triangle ABC$.
• Option 3: $\triangle A'B'C'$ is the image of $\triangle ABC$ after reflection. Since reflection is a rigid motion and preserves angle measures, if $\triangle ABC$ is right (has a 90 - degree angle), $\triangle A'B'C'$ will also be right because the angle measures are unchanged.

Answer:

$\triangle A'B'C'$ is right because it is the image of $\triangle ABC$ under a reflection, and reflections preserve angle - measures.