Question

△abc≅△xyz. complete each congruence statement.
1 fill in the blank 1 point
∠a≅∠type your answer...
2 fill in the blank 1 point
xy≅type your answer...
3 fill in the blank 1 point
∠z≅∠type your answer...
4 fill in the blank 1 point
bc≅type your answer...
5 fill in the blank 1 point
△zyx≅△type your answer...
6 fill in the blank 1 point
△yzx≅△type your answer...

Explanation:

Step1: Identify corresponding parts in congruent triangles

When \(\triangle ABC\cong\triangle XYZ\), the order of the letters in the congruence statement gives the correspondence. For angles, \(\angle A\) corresponds to \(\angle X\) (first - letter correspondence in \(\triangle ABC\) and \(\triangle XYZ\)).

Step2: Identify corresponding sides

For sides, \(\overline{XY}\) in \(\triangle XYZ\) corresponds to \(\overline{AB}\) in \(\triangle ABC\) (first - two letters in the triangle names).

Step3: Identify corresponding angles

\(\angle Z\) in \(\triangle XYZ\) corresponds to \(\angle C\) in \(\triangle ABC\) (last - letter correspondence).

Step4: Identify corresponding sides

\(\overline{BC}\) in \(\triangle ABC\) corresponds to \(\overline{YZ}\) in \(\triangle XYZ\) (last - two letters in the triangle names).

Step5: Rewrite the congruence statement

For \(\triangle ZYX\), we use the correspondence. Since \(\triangle ABC\cong\triangle XYZ\), \(\triangle ZYX\cong\triangle CBA\) (reversing the order of letters based on vertex correspondence).

Step6: Rewrite the congruence statement

For \(\triangle YZX\), \(\triangle YZX\cong\triangle BCA\) (using the vertex - to - vertex correspondence from \(\triangle ABC\cong\triangle XYZ\)).

Answer:

1. \(X\)
2. \(\overline{AB}\)
3. \(C\)
4. \(\overline{YZ}\)
5. \(CBA\)
6. \(BCA\)