Question

practice: proving triangles congruent using asa and aas

\\(\triangle abc \cong \triangle def\\) because they meet the congruence criterion for asa. select all the transformations used in the sequence to map \\(\triangle abc\\) onto \\(\triangle def\\).

Explanation:

⚡ Using what you learned: congruence criteria for triangles (sss, sas, asa, aas, hl)

Step 1: Identify Given Congruent Parts

From the markings on the triangles \(\triangle ABC\) and \(\triangle DEF\):

• Angle \(B\) has a double arc marking, which matches the double arc marking at angle \(E\):

$$ \angle B \cong \angle E $$

• Side \(AB\) has a single tick mark, which matches the single tick mark on side \(DE\):

$$ AB \cong DE $$

• Angle \(A\) has a triple arc marking, which matches the triple arc marking at angle \(D\):

$$ \angle A \cong \angle D $$

Step 2: Determine the Congruence Criterion

The congruent parts are:

1. An angle (\(\angle B \cong \angle E\))
2. The included side (\(AB \cong DE\))
3. Another angle (\(\angle A \cong \angle D\))

Since the congruent side is directly between the two congruent angles, the triangles are congruent by the Angle-Side-Angle (ASA) postulate.

Answer:

\(\triangle ABC \cong \triangle DEF\) by the ASA (Angle-Side-Angle) congruence criterion.