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{rj}) c) (angle r=angle t) d) (angle j=angle a)

Explanation:

Step1: Recall properties of translation and reflection

Translation and reflection are rigid transformations. Rigid transformations 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 \(\triangle JOE\cong\triangle CAT\), \(OE = CT
eq AT\) (in general).

• Option B:

Since \(\triangle JOE\cong\triangle BRI\), \(JE = RI\).

• Option C:

Since \(\triangle BRI\cong\triangle CAT\), \(\angle R=\angle C
eq\angle T\) (in general).

• Option D:

Since \(\triangle JOE\cong\triangle CAT\), \(\angle J=\angle C
eq\angle A\) (in general).

Answer:

B. \(\overline{JE}=\overline{RI}\)