Question

which two triangles are congruent by the sas theorem? complete the congruence statement.

Explanation:

Step1: Recall SAS Congruence Rule

SAS (Side-Angle-Side) requires two pairs of corresponding sides to be congruent, and the included angle (the angle between the two sides) to be congruent.

Step2: Analyze Triangle $\triangle QRS$

In $\triangle QRS$:

• Side $QR$ (marked with double hash marks), side $RS$ (marked with single hash mark)
• Included angle: $\angle R$ (the angle between $QR$ and $RS$)

Step3: Analyze Triangle $\triangle GEF$

In $\triangle GEF$:

• Side $GE$ (marked with single hash mark), side $EF$ (marked with double hash marks)
• Included angle: $\angle G$ (the angle between $GE$ and $EF$)

Step4: Analyze Triangle $\triangle BCD$

In $\triangle BCD$:

• Side $BC$ (marked with double hash marks), side $BD$ (marked with single hash mark)
• Included angle: $\angle B$ (the angle between $BC$ and $BD$)

Step5: Match Corresponding SAS Parts

For $\triangle QRS$ and $\triangle BCD$:

1. $QR \cong BC$ (double hash marks, congruent sides)
2. $\angle R \cong \angle B$ (marked congruent angles, included angles)
3. $RS \cong BD$ (single hash marks, congruent sides)

This satisfies the SAS Congruence Theorem.

Answer:

$\triangle QRS \cong \triangle BCD$