Question

explore exploring congruence of parts of transformed figures
read explore and complete the following (adapted from lesson 3.3). show all your work.
△abc and △def are congruent, meaning △abc can be mapped onto △def by a sequence of rigid motions
rigid motions preserve the measure of the sides and the measure of the angles. determine which sides and angles from △def match up with △abc by completing the following.
$overline{ab}\tosquare$ $overline{bc}\tosquare$ $overline{ac}\tosquare$
$angle a\tosquare$ $angle b\tosquare$ $angle c\tosquare$
if you know that △abc≅△def, what six congruence statements about segments and angles can you write?
examples of congruence statements: $overline{fh}congoverline{hj}$ $angle fcongangle j$

Explanation:

Step1: Recall congruent - triangle properties

In congruent triangles, corresponding sides and angles are equal. Since \(\triangle ABC\cong\triangle DEF\), the order of the vertices gives the correspondence.

Step2: Match the sides

\(\overline{AB}\) corresponds to \(\overline{DE}\), \(\overline{BC}\) corresponds to \(\overline{EF}\), and \(\overline{AC}\) corresponds to \(\overline{DF}\).

Step3: Match the angles

\(\angle A\) corresponds to \(\angle D\), \(\angle B\) corresponds to \(\angle E\), and \(\angle C\) corresponds to \(\angle F\).

Step4: Write congruence statements

The six congruence statements are \(\overline{AB}\cong\overline{DE}\), \(\overline{BC}\cong\overline{EF}\), \(\overline{AC}\cong\overline{DF}\), \(\angle A\cong\angle D\), \(\angle B\cong\angle E\), \(\angle C\cong\angle F\).

Answer:

\(\overline{AB}\to\overline{DE}\), \(\overline{BC}\to\overline{EF}\), \(\overline{AC}\to\overline{DF}\), \(\angle A\to\angle D\), \(\angle B\to\angle E\), \(\angle C\to\angle F\)
\(\overline{AB}\cong\overline{DE}\), \(\overline{BC}\cong\overline{EF}\), \(\overline{AC}\cong\overline{DF}\), \(\angle A\cong\angle D\), \(\angle B\cong\angle E\), \(\angle C\cong\angle F\)