Question

In figure (AP) = ( AQ ), ∠ABQ ≅ ∠ACP.

State the test and the correspondence of the vertices by

which ∆ABQ and ∆ACP are congruent write the remaining

congruent parts.​

Answer 1

Answer:

The remaining congruent parts are:

   Side AB ≅ side AC (corresponding sides of congruent triangles)

   Angle BQA ≅ angle CPA (corresponding angles of congruent triangles)

Step-by-step explanation:

The given information suggests that we have two triangles, ∆ABQ and ∆ACP, in which the following conditions are true:

   (AP) = (AQ) (sides AP and AQ are congruent)

   ∠ABQ ≅ ∠ACP (angle ABQ is congruent to angle ACP)

In order to prove that the two triangles are congruent, we need to use a congruence test. The test that applies here is the Side-Angle-Side (SAS) test, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

So, using the SAS test, we can say that ∆ABQ ≅ ∆ACP. The correspondence of the vertices that makes the two triangles congruent is:

A → A (common vertex)

B → C (corresponding vertices with congruent angles)

Q → P (corresponding vertices with congruent sides)

Therefore, the remaining congruent parts are:

   Side AB ≅ side AC (corresponding sides of congruent triangles)

   Angle BQA ≅ angle CPA (corresponding angles of congruent triangles)

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