Question

1. given $\triangle abc\cong\triangle def$, name three pairs of congruent sides.
2. given $\triangle mno\cong\triangle pqr$, name three pairs of congruent angles.
3. copy the congruent triangles shown at the right. then label the vertices of your triangles so that $\triangle ruv\cong\triangle tnf$. identify all pairs of congruent corresponding angles and corresponding sides.

Explanation:

Step1: Identify congruent triangles' sides

For congruent triangles \( \triangle ABC\cong\triangle DEF\), corresponding vertices are \(A\) with \(D\), \(B\) with \(E\), \(C\) with \(F\).
So, \(AB\cong DE\), \(BC\cong EF\), \(AC\cong DF\).

Step2: Identify congruent triangles' angles

For congruent triangles \( \triangle MNO\cong\triangle PQR\), corresponding vertices are \(M\) with \(P\), \(N\) with \(Q\), \(O\) with \(R\).
So, \( \angle M\cong\angle P\), \( \angle N\cong\angle Q\), \( \angle O\cong\angle R\).

Step3: Label and identify for \( \triangle RUV\cong\triangle TNF\)

Corresponding vertices: \(R\) with \(T\), \(U\) with \(N\), \(V\) with \(F\).
Sides: \(RU\cong TN\), \(UV\cong NF\), \(RV\cong TF\).
Angles: \( \angle R\cong\angle T\), \( \angle U\cong\angle N\), \( \angle V\cong\angle F\).

Answer:

1. \(AB\cong DE\), \(BC\cong EF\), \(AC\cong DF\).
2. \( \angle M\cong\angle P\), \( \angle N\cong\angle Q\), \( \angle O\cong\angle R\).
3. Sides: \(RU\cong TN\), \(UV\cong NF\), \(RV\cong TF\); Angles: \( \angle R\cong\angle T\), \( \angle U\cong\angle N\), \( \angle V\cong\angle F\).