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In triangles ABC and PQR, angle A is congruent to angle P, angle B is congruent to angle Q, and side AC is congruent to side PR.

Show that triangle ABC is congruent to triangle PQR using the ASA (Angle-Side-Angle) congruence test.

Answer :

To show that triangle [tex]ABC[/tex] is congruent to triangle [tex]PQR[/tex] using the Angle-Side-Angle (ASA) Congruence Postulate, we need to verify that two angles and the included side in one triangle are congruent to two angles and the included side in the other triangle.

Given conditions:

  1. [tex]\angle A \cong \angle P[/tex]

  2. [tex]\angle B \cong \angle Q[/tex]

  3. Side [tex]AC \cong PR[/tex]

According to the ASA Postulate, if two angles and the included side in one triangle are congruent to two angles and the included side in another triangle, the two triangles are congruent.

Steps to Show Congruence:

  1. Identify Congruent Angles and Included Side:

    • We have [tex]\angle A \cong \angle P[/tex] and [tex]\angle B \cong \angle Q[/tex]. The side between these two angles in [tex]\triangle ABC[/tex] is [tex]AC[/tex], and the side between the corresponding two angles in [tex]\triangle PQR[/tex] is [tex]PR[/tex].

  2. Check Included Side Congruence:

    • We also have [tex]AC \cong PR[/tex], which means the sides between the pairs of angles are congruent.

  3. Apply ASA Postulate:

    • Since two angles and the included side in [tex]\triangle ABC[/tex] ([tex]\angle A[/tex], [tex]\angle B[/tex], and [tex]AC[/tex]) are congruent to two angles and the included side in [tex]\triangle PQR[/tex] ([tex]\angle P[/tex], [tex]\angle Q[/tex], and [tex]PR[/tex]), we can conclude by the ASA Postulate that [tex]\triangle ABC \cong \triangle PQR[/tex].

This application of the ASA Postulate demonstrates that the given conditions are sufficient to prove the congruence of the two triangles.

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Rewritten by : Jeany

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