Question

11/8 - congruent figures
if ( \triangle abccong\triangle fed ), complete each statement.

1. ( \triangle acbcong\trianglesquare ) 2. ( angle bconganglesquare )
2. ( \triangle bcacong\trianglesquare ) 4. ( overline{ac}congsquare )
3. ( angle aconganglesquare ) 6. ( overline{cb}congsquare )

Explanation:

Step1: Recall congruent triangle properties

Congruent triangles have corresponding parts equal. If \(\triangle ABC\cong\triangle FED\), then \(A\) corresponds to \(F\), \(B\) corresponds to \(E\), and \(C\) corresponds to \(D\).

Step2: Solve for \(\triangle ACB\cong\triangle\)

For \(\triangle ACB\), using correspondence \(A - F\), \(C - D\), \(B - E\), so \(\triangle ACB\cong\triangle FDE\)

Step3: Solve for \(\angle B\cong\angle\)

Since \(B\) corresponds to \(E\), \(\angle B\cong\angle E\)

Step4: Solve for \(\triangle BCA\cong\triangle\)

Using correspondence \(B - E\), \(C - D\), \(A - F\), so \(\triangle BCA\cong\triangle EDF\)

Step5: Solve for \(\overline{AC}\cong\)

\(A\) corresponds to \(F\), \(C\) corresponds to \(D\), so \(\overline{AC}\cong\overline{FD}\)

Step6: Solve for \(\angle A\cong\angle\)

\(A\) corresponds to \(F\), so \(\angle A\cong\angle F\)

Step7: Solve for \(\overline{CB}\cong\)

\(C\) corresponds to \(D\), \(B\) corresponds to \(E\), so \(\overline{CB}\cong\overline{DE}\)

Answer:

1. \(FDE\)
2. \(E\)
3. \(EDF\)
4. \(FD\)
5. \(F\)
6. \(DE\)