Question

congruence statements
complete the congruence statement for each pair of triangles.
1)

\\( \triangle a b c \cong \\)
2)

\\( \triangle u v w \cong \\)
3)

\\( \triangle p q r \cong \\)
4)

\\( \triangle k l m \cong \\)
5)
6)

Explanation:

Step1: Identify corresponding vertices for \(\triangle ABC\) and \(\triangle EDF\)

• In \(\triangle ABC\) and \(\triangle EDF\), \(\angle A=\angle D = 90^{\circ}\), \(\angle B=\angle F\), \(\angle C=\angle E\)
• And the sides: \(AB = DF\), \(BC=FE\), \(AC = DE\)
• So \(\triangle ABC\cong\triangle FDE\)

Step2: Identify corresponding vertices for \(\triangle UVW\) and \(\triangle YZX\)

• In \(\triangle UVW\) and \(\triangle YZX\), \(\angle U=\angle Y\), \(\angle V=\angle Z\), \(\angle W=\angle X\)
• And the sides: \(UV = YZ\), \(VW=ZX\), \(WU = XY\)
• So \(\triangle UVW\cong\triangle YZX\)

Step3: Identify corresponding vertices for \(\triangle PQR\) and \(\triangle RST\)

• In \(\triangle PQR\) and \(\triangle RST\), \(\angle P=\angle S\), \(\angle Q=\angle T\), \(\angle PRQ=\angle RTS\)
• And the sides: \(PQ = ST\), \(QR=TR\), \(PR = RS\)
• So \(\triangle PQR\cong\triangle STR\)

Step4: Identify corresponding vertices for \(\triangle KLM\) and \(\triangle GLJ\)

• In \(\triangle KLM\) and \(\triangle GLJ\), \(\angle K=\angle G\), \(\angle L=\angle L\), \(\angle M=\angle J\)
• And the sides: \(KL = GL\), \(LM=LJ\), \(MK = JG\)
• So \(\triangle KLM\cong\triangle GLJ\)

Answer:

1. \(\triangle FDE\)
2. \(\triangle YZX\)
3. \(\triangle STR\)
4. \(\triangle GLJ\)