Question

charlie is using rigid transformations to justify the sss congruence theorem. he started with △abc and △def that have three pairs of congruent sides. he translated and then rotated △abc to create △a b c such that (overline{a b }) coincides with (overline{de}). he then constructed the circles shown in the image and labeled points 1 and 2. why are points 1 and 2 significant? option #1: they are the only points in the plane that are both a distance ef away from point e and a distance df away from point d. option #2: they are the only points in the plane that are both a distance ed away from point e and a distance fe away from point f. option #3: they are the only points in the plane that are both a distance ef away from point e and a distance fe away from point f. (1 point) option # best describes the significance of points 1 and 2.

Explanation:

To justify SSS Congruence, after aligning \( A''B'' \) with \( DE \), the third vertex \( C'' \) must satisfy \( B''C'' = EF \) (distance from \( E \)) and \( A''C'' = DF \) (distance from \( D \)). Circles centered at \( E \) (radius \( EF \)) and \( D \) (radius \( DF \)) intersect at two points, which are the only such points.

Answer:

Option #1: They are the only points in the plane that are both a distance \( EF \) away from point \( E \) and a distance \( DF \) away from point \( D \)