Question

state what additional information is required in order to know that the triangles are congruent for the reason given.

1. sss
2. sss
3. sss
4. sss
5. sss
6. sss

Explanation:

Step1: Recall SSS (Side - Side - Side) Congruence Criterion

The SSS congruence criterion states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Step2: Analyze Each Pair of Triangles

• 11) We need to check the sides of the two triangles. Let the two triangles be \(\triangle KJL\) and \(\triangle WJL\). We already know some sides. For SSS, we need \(KL = WJ\).
• 12) Let the two triangles be \(\triangle DXZ\) and \(\triangle YXZ\). We need \(DZ=YZ\).
• 13) Let the two triangles be \(\triangle GHF\) and \(\triangle SHF\). We need \(GH = SF\).
• 15) Let the two triangles be \(\triangle RSQ\) and \(\triangle CAB\). We need \(RS = AB\) and \(SQ=CA\).
• 16) Let the two triangles be \(\triangle QGE\) and \(\triangle FGE\). We need \(QE = FE\).

Answer:

1. \(KL = WJ\)
2. \(DZ = YZ\)
3. \(GH=SF\)
4. \(RS = AB\) and \(SQ = CA\)
5. \(QE=FE\)