Question

1. a student draws △xyz and △efg so that m∠x = m∠e = 29.5°, xy = ef = 47 mm, and xz = eg = 63 mm. which criteria can the student use to prove that the triangles are congruent?

a ssa congruence criteria
b sas congruence criteria
c asa congruence criteria
d aas congruence criteria

Explanation:

Step1: Recall the congruence criteria

• SSA (Side - Side - Angle): Not a valid congruence criterion in general as it can lead to ambiguous cases.
• ASA (Angle - Side - Angle): Requires two angles and the included side.
• SAS (Side - Angle - Side): Requires two sides and the included angle. Here, we have \(XY = EF\) (one side), \(\angle X=\angle E\) (one angle), and \(XZ = EG\) (another side). The angle \(\angle X\) is between \(XY\) and \(XZ\), and \(\angle E\) is between \(EF\) and \(EG\).
• AAS (Angle - Angle - Side): Requires two angles and a non - included side.

Answer:

B. SAS congruence criteria