Question

state what additional information is needed to prove the triangles are congruent using sas:

\\(uw \cong km\\)
\\(\angle w \cong \angle k\\)
\\(vw \cong vm\\)
not possible

Explanation:

Identify given congruent parts

Using the Triangle Congruence Postulates knowledge point, we analyze the markings on the given triangles \(\Delta UWV\) and \(\Delta KMV\).
The tick marks indicate:

$$ UV \cong KV $$

Identify vertical angles

Using the Vertical Angles Theorem knowledge point, we find the congruent angles formed by the intersecting lines \(UK\) and \(WM\) at vertex \(V\):

$$ \angle UVW \cong \angle KVM $$

Determine required part for SAS

Using the SAS Congruence knowledge point, we need two sides and their included angle to be congruent.
We currently have:

• Side: \(UV \cong KV\)
• Included Angle: \(\angle UVW \cong \angle KVM\)

For these angles to be the included angles between two sides, we need the second pair of adjacent sides forming the angle to be congruent:

$$ VW \cong VM $$

Answer:

• (A) \(UW \cong KM\)
• (B) \(\angle W \cong \angle K\)
• (C) \(VW \cong VM\) (Correct answer)
• (D) not possible