Question

show that the polygons are congruent by identifying all the congruent corresponding parts. then complete the congruence statement.\
$\angle j \cong \angle$ select choice ;\
$\angle jkm \cong \angle$ select choice ;\
$\angle kmj \cong \angle$ select choice ;\
segment $kj \cong$ segment select choice ;\
segment $kl \cong$ segment select choice ;

Explanation:

Step1: Analyze ∠J ≅ ∠?

In the diagram, \( JKLM \) (assuming the figure is a rectangle or congruent triangles) has right angles. \( \angle J \) is a right angle, so \( \angle J \cong \angle L \) (since \( \angle L \) is also a right angle, as seen from the diagram's markings).

Step2: Analyze ∠JKM ≅ ∠?

Looking at the triangles \( \triangle JKM \) and \( \triangle LMK \), \( \angle JKM \) and \( \angle KML \) are alternate interior angles (or corresponding angles in congruent triangles). So \( \angle JKM \cong \angle KML \).

Step3: Analyze ∠KMJ ≅ ∠?

Similarly, \( \angle KMJ \) and \( \angle MKL \) are corresponding angles in the congruent triangles, so \( \angle KMJ \cong \angle MKL \).

Step4: Analyze segment KJ ≅ segment?

From the diagram, \( KJ \) and \( LM \) are marked as congruent (or in a rectangle, opposite sides are equal, so \( KJ \cong LM \)).

Step5: Analyze segment KL ≅ segment?

In the figure, \( KL \) and \( JM \) are congruent (opposite sides of a rectangle or congruent triangles' sides), so \( KL \cong JM \).

Answer:

• \( \angle J \cong \angle L \)
• \( \angle JKM \cong \angle KML \)
• \( \angle KMJ \cong \angle MKL \)
• segment \( KJ \cong \) segment \( LM \)
• segment \( KL \cong \) segment \( JM \)