Question

1. can you prove the triangles congruent? if so, write the congruence statement and name the postulate you would use. if not, write not enough information and tell what other information you would need.

a)
b)
c)

Explanation:

Part (a)

Step1: Identify Given Information

In triangles \( \triangle ANG \) and \( \triangle RWT \), we see that one pair of sides is marked congruent (single tick), another pair of sides is marked congruent (double tick), and the included angles (the right angles, as indicated by the right angle symbol at \( N \) and \( W \)) are congruent.

Step2: Apply SAS Postulate

The Side - Angle - Side (SAS) postulate 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. So, \( \triangle ANG \cong \triangle RWT \) by SAS.

Step1: Analyze Given Information

In triangles \( \triangle HY D \) and \( \triangle KPT \), we have two pairs of sides marked congruent (the tick marks on the sides). But we do not know if the included angles are congruent or if the third pair of sides is congruent. We only have two sides of each triangle marked as congruent, but no information about the angle between them or the third side.

Step2: Determine What's Needed

To prove congruence, we would need either the included angle between the two marked sides to be congruent (to use SAS) or the third side to be congruent (to use SSS). Since we don't have that, there's not enough information. We need either the included angle or the third side to be congruent.

Step1: Identify Given Information

In triangles \( \triangle EJF \) and \( \triangle SVF \), we see that \( E F=FV \) (marked with double ticks), \( EJ = SV \) (marked with single ticks), and \( JF=SF \) (marked with single ticks).

Step2: Apply SSS Postulate

The Side - Side - Side (SSS) postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. So, \( \triangle EJF\cong\triangle SVF \) by SSS.

Answer:

Yes, \( \triangle ANG \cong \triangle RWT \) by SAS (Side - Angle - Side) postulate.

Part (b)