Question

<wck aa <ckw sas corresponding sides proportional reflexive property alternate interior angles corresponding angles corresponding angles proportional l k w statement reason \\(\overline{dl} \parallel \overline{ck}\\) given \\(\angle dlk \cong \square\\) \\(\angle w \cong \angle w\\) \\(\triangle dlw \sim \triangle ckw\\) \\(\frac{dw}{lw} = \frac{cw}{kw}\\)

Explanation:

Step1: Identify Angle Relationship

Since \( \overline{DL} \parallel \overline{CK} \), by Alternate Interior Angles, \( \angle DLK \cong \angle CKW \).

Step2: Reflexive Property for \( \angle W \)

\( \angle W \cong \angle W \) is by Reflexive Property (an angle is congruent to itself).

Step3: Prove Triangle Similarity

With two pairs of congruent angles (\( \angle DLK \cong \angle CKW \) and \( \angle W \cong \angle W \)), by AA (Angle - Angle) Similarity Criterion, \( \triangle DLW \sim \triangle CKW \).

Step4: Corresponding Sides Proportional

For similar triangles \( \triangle DLW \) and \( \triangle CKW \), corresponding sides are proportional, so \( \frac{DW}{LW}=\frac{CW}{KW} \).

Answer:

• \( \angle DLK \cong \boldsymbol{\angle CKW} \) (Reason: Alternate Interior Angles)
• \( \angle W \cong \angle W \) (Reason: Reflexive Property)
• \( \triangle DLW \sim \triangle CKW \) (Reason: AA Similarity)
• \( \frac{DW}{LW}=\frac{CW}{KW} \) (Reason: Corresponding Sides Proportional)