Question

1. in the diagram below, △bri is the image of △joe after a translation. triangle cat is the image of △bri after a line reflection. which one of the following statements is always true? a) \overline{oe}=\overline{at} b) \overline{je}=\overline{ri} c) \angle r=\angle t d) \angle j=\angle a

Explanation:

Step1: Recall properties of translation and reflection

Translation and reflection are rigid motions. Rigid motions preserve side - lengths and angles. So, \(\triangle JOE\cong\triangle BRI\) (because of translation) and \(\triangle BRI\cong\triangle CAT\) (because of reflection). By the transitive property of congruence, \(\triangle JOE\cong\triangle CAT\).

Step2: Analyze each option

• Option A:

Since \(\triangle JOE\cong\triangle CAT\), \(OE = CT
eq AT\) (corresponding parts of congruent triangles).

• Option B:

Since \(\triangle JOE\cong\triangle BRI\), \(JE = BI
eq RI\) (corresponding parts of congruent triangles).

• Option C:

Since \(\triangle BRI\cong\triangle CAT\), \(\angle R=\angle C
eq\angle T\) (corresponding parts of congruent triangles).

• Option D:

Since \(\triangle JOE\cong\triangle CAT\), \(\angle J=\angle A\) (corresponding parts of congruent triangles).

Answer:

D. \(\angle J=\angle A\)