Question

Statement
Reason


L1 /4 and L3 46
::
ASA Congruence Theorem
#: a b ande
CPCTC Theorem
:
XY ~XY
:: Reflexive Property of Congruence
: YW e XZ and WX e ZY
AYWX 2 AXZY
::


:: Given


:: Alternate Interior Angles Theorem

Answer 1

The content you provided seems to be an outline or notes regarding a geometric proof using congruence theorems, specifically relating to triangles and proportional segments. Based on the statements and reasons you've included, I can help you organize them into a clearer format for a proof. Here's how you might lay it out:

### Proof Outline

**Statement 1:** \( L1 \parallel L3 \)
**Reason 1:** Given

**Statement 2:** \( \angle A \cong \angle B \) and \( \angle Y \cong \angle Z \)
**Reason 2:** Corresponding Angles Postulate (if lines are parallel, then corresponding angles are congruent)

**Statement 3:** \( \triangle AYW \cong \triangle AXZ \)
**Reason 3:** ASA (Angle-Side-Angle) Congruence Theorem

**Statement 4:** \( XY \cong WX \) and \( YW \cong XZ \)
**Reason 4:** CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

**Statement 5:** \( XY \sim XZ \)
**Reason 5:** Reflexive Property of Congruence (since \( XY \) and \( XZ \) are segments included in corresponding triangles)

**Statement 6:** \( YW \equiv XZ \) and \( WX \equiv ZY \)
**Reason 6:** Given (but typically would also rely on established relationships or congruencies)

**Statement 7:** Conclusion based on \( AYWX \cong AXZY \)
**Reason 7:** By the Alternate Interior Angles Theorem (establishes angle relationships further, supporting triangle congruence)

This format highlights the logical sequence of reasoning and corresponds each statement to its justification, clarifying the relationships between the components of your geometric proof. Adjustments can be made based on specific conclusions or additional context.