Question

show that the polygons are congruent by identifying all congruent corresponding parts. then write a congruence statement. 12. 13. 14. 15. 16. 17.

Explanation:

Step1: Identify congruent sides

For example, in problem 12, if we assume $\triangle ABC$ and $\triangle JKL$, we look at the markings on the sides. If $AB = JK$, $BC=KL$, and $AC = JL$ (as indicated by the equal - length markings).

Step2: Identify congruent angles

In $\triangle ABC$ and $\triangle JKL$, if $\angle A=\angle J$, $\angle B=\angle K$, and $\angle C=\angle L$ (as indicated by the angle - congruence markings).

Step3: Write congruence statement

The congruence statement for $\triangle ABC$ and $\triangle JKL$ is $\triangle ABC\cong\triangle JKL$. We follow the same process for other polygon pairs in the problems. For each pair of polygons, match the corresponding congruent sides and angles based on the markings on the figures and then write the congruence statement in the form of polygon $1\cong$ polygon $2$, making sure to list the vertices in corresponding order.

Answer:

For problem 12: If $AB = JK$, $BC = KL$, $AC=JL$, $\angle A=\angle J$, $\angle B=\angle K$, $\angle C=\angle L$, then $\triangle ABC\cong\triangle JKL$.
For problem 13: Identify congruent sides and angles using markings. Let's assume sides and angles are congruent as marked. Then write the congruence statement for the two - triangle combination (e.g., if $\triangle ABC$ and $\triangle DCB$, and all corresponding parts are congruent, $\triangle ABC\cong\triangle DCB$).
For problem 14: Identify congruent sides and angles of the quadrilaterals $JKLM$. If all corresponding sides and angles are congruent as marked, write the congruence statement (e.g., $JKLM\cong$ another quadrilateral with vertices in corresponding order).
For problem 15: For right - angled triangles $\triangle EFG$ and $\triangle JKL$, if all corresponding sides and angles are congruent as marked, write the congruence statement $\triangle EFG\cong\triangle JKL$.
For problem 16: Identify congruent sides and angles of the two - triangle combination within the quadrilateral. If all corresponding parts are congruent as marked, write the congruence statement (e.g., $\triangle ABC\cong\triangle ADC$).
For problem 17: For $\triangle RST$ and $\triangle SUT$, if all corresponding sides and angles are congruent as marked, write the congruence statement $\triangle RST\cong\triangle SUT$.