Question

1. sas

a) additional known statement:

reason:

b) information still needed:

to prove the \\( \delta \cong \\) by \\( \underline{sas} \\)

Explanation:

Step1: Identify the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze the given triangles

We know that for \(\triangle L M\) and \(\triangle GIH\), we have two pairs of sides congruent (from the markings).

Part a)

• Additional Known Statement: \(\angle L=\angle G\)
• Reason: For the SAS criterion, we need the included angle between the two pairs of congruent sides. If \(\angle L\) and \(\angle G\) are the included angles between the two pairs of congruent sides (from the side markings in the triangles), then this is a valid additional statement.

Part b)

• Information still needed: The included angle between the two pairs of congruent sides (if \(\angle L\) and \(\angle G\) are not already given). If we assume that the two pairs of sides are \(LM = GH\) and \(LI=GI\) (from the markings), then the included angle (either \(\angle L\) and \(\angle G\) depending on the correspondence of the sides) is needed.

Answer:

a) Additional Known Statement: \(\angle L=\angle G\); Reason: SAS criterion requires included angle between two pairs of congruent sides.
b) Information still needed: The measure of the included angle (e.g., \(\angle L\) and \(\angle G\) if not already known) between the two pairs of congruent sides.