Question

Complete the proofs using the most appropriate method. Some may require CPCTC: Given: KN≅ML, KN || LM Prove: ΔKLN≅ΔMNL *there is five steps*

Answer 1

To prove the congruence of ΔKLN and ΔMNL, alternate interior angles and the Reflexive Property were used, followed by applying the SAS Postulate and concluding with CPCTC.

Step-by-step explanation:

To prove that ΔKLN is congruent to ΔMNL, we can use the given information and the properties of parallel lines and congruent triangles.

1. Given: KN≡ML and KN || ML, by definition of parallel lines, this implies that alternate interior angles are congruent. Therefore, ∠KLN≡∠MLN.
2. By the Reflexive Property of congruence, which states that any geometric figure is congruent to itself, segment LN≡LN.
3. From step 1, we have two pairs of congruent angles (∠KLN≡∠MLN) and from the given KN≡ML, we now have two pairs of congruent sides (KN≡ML and LN≡LN).
4. Since we have two pairs of sides and the angle between them congruent, we can use the Side-Angle-Side (SAS) Postulate for triangle congruence to conclude ΔKLN≡ΔMNL.
5. Lastly, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), all other corresponding parts of the triangles are congruent, completing the proof.

This sequence of steps properly applies geometric postulates and theorems to prove congruence between ΔKLN and ΔMNL.