Question

Show that polygons are congruent by identifying all congruent corresponding parts by writing congruent statements for the parts. Then write an overall triangle congruence statement.

Answer 1

To show polygons, especially triangles, are congruent, all corresponding sides and angles must be proven congruent, and the overall congruence statement would be the notation of one triangle being congruent to the other.

Step-by-step explanation:

To show that two polygons are congruent, we must demonstrate that all corresponding sides and angles are congruent. When considering triangles, if we have two congruent triangles, we can write the congruence statement by matching each corresponding side and angle. For instance, if triangle ABC is congruent to triangle DEF, we would say that side AB is congruent to side DE, AC is congruent to DF, and BC is congruent to EF. Similarly, we would match the angles such that ∠A is congruent to ∠D, ∠B is congruent to ∠E, and ∠C is congruent to ∠F.

The overall triangle congruence statement would then be written as ΔABC ≅ ΔDEF. This indicates that the two triangles are congruent and all corresponding parts are congruent as well. Congruence can be proved using various methods such as Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL), depending on the given information.