Question

name date determine if the triangles are congruent. write the triangle congruence statements and name the postulate or theorem you would use. if they are not congruent, write not enough information. use sss or sas 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

Explanation:

Step1: Analyze triangle congruence for each pair

• 1) For \(\triangle ABC\) and \(\triangle DEF\), we have \(AB = DE\), \(AC = DF\), but no information about the included angles. So, not enough information.
• 2) For \(\triangle JKL\) and \(\triangle JML\), \(JK = JM\), \(KL = ML\), \(JL=JL\) (common side). By SSS (Side - Side - Side) congruence postulate, \(\triangle JKL\cong\triangle JML\).
• 3) For \(\triangle RST\) and \(\triangle WXY\), we have \(RS = WX\), \(ST = XY\), but no information about the included angles. So, not enough information.
• 4) For \(\triangle VU\) and \(\triangle PU\), \(VU = PU\), \(UV = UV\) (common side), but no information about the included angles. So, not enough information.
• 5) For \(\triangle ABC\) and \(\triangle ADC\), \(AB = AD\), \(BC = DC\), \(\angle ACB=\angle ACD\) (common angle). By SAS (Side - Angle - Side) congruence postulate, \(\triangle ABC\cong\triangle ADC\).
• 6) For \(\triangle EFH\) and \(\triangle GFH\), \(EF = GH\), \(FH = FH\) (common side), \(EH = FG\). By SSS (Side - Side - Side) congruence postulate, \(\triangle EFH\cong\triangle GFH\).
• 7) For \(\triangle NTA\) and \(\triangle EDR\), we have \(NT = ED\), \(TA = DR\), but no information about the included angles. So, not enough information.
• 8) For \(\triangle ABC\) and \(\triangle ADC\), \(AB = AD\), \(BC = DC\), \(AC = AC\) (common side). By SSS (Side - Side - Side) congruence postulate, \(\triangle ABC\cong\triangle ADC\).
• 9) For \(\triangle AFE\) and \(\triangle BFE\), \(AF = BF\), \(FE = FE\) (common side), but no information about the included angles. So, not enough information.
• 10) For \(\triangle EFG\) and \(\triangle DCG\), \(EG = CG\), \(FG = DG\), \(\angle EGF=\angle DCG\) (vertical angles). By SAS (Side - Angle - Side) congruence postulate, \(\triangle EFG\cong\triangle DCG\).

Answer:

1. not enough information
2. \(\triangle JKL\cong\triangle JML\) (SSS)
3. not enough information
4. not enough information
5. \(\triangle ABC\cong\triangle ADC\) (SAS)
6. \(\triangle EFH\cong\triangle GFH\) (SSS)
7. not enough information
8. \(\triangle ABC\cong\triangle ADC\) (SSS)
9. not enough information
10. \(\triangle EFG\cong\triangle DCG\) (SAS)