Question

given $delta abc$, describe how to construct $delta pqr$ congruent to $delta abc$ using each of the following combinations.
a. two sides of $delta abc$ and an angle included between these two sides
b. the three sides of $delta abc$
c. two angles and a side included between these angles
c. choose the correct answer below
a. copy $overline{bc}$ from $delta abc$ to form $overline{pr}$. then copy $angle b$ to use for $angle p$ and copy $angle c$ to use for $angle r$. draw lines for the two remaining sides, $overline{pq}$ and $overline{qr}$. the intersection of the two lines is the vertex q of triangle $delta pqr$
b. copy $overline{bc}$ from $delta abc$ to form $overline{qr}$. then copy $angle b$ to use for $angle q$ and copy $angle c$ to use for $angle r$. draw lines for the two remaining sides, $overline{pq}$ and $overline{pr}$. the intersection of the two lines is the vertex p of triangle $delta pqr$
c. copy $overline{bc}$ from $delta abc$ to form $overline{pq}$. then copy $angle b$ to use for $angle p$ and copy $angle c$ to use for $angle q$. draw lines for the two remaining sides, $overline{pr}$ and $overline{qr}$. the intersection of the two lines is the vertex r of triangle $delta pqr$

Explanation:

Step1: Recall ASA (Angle - Side - Angle) congruence

The ASA congruence criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent.

Step2: Analyze the construction steps

We need to copy the side and the two adjacent angles. When constructing $\triangle PQR$ congruent to $\triangle ABC$ using two angles and the included side, we first copy the side. Then we copy the two angles adjacent to that side.
For the given problem, if we consider the side - angle - angle combination, we should copy a side from $\triangle ABC$ and then the two angles adjacent to that side to form $\triangle PQR$.
If we copy $\overline{BC}$ from $\triangle ABC$ to form $\overline{PR}$ (the included side), then copy $\angle B$ to use for $\angle P$ and copy $\angle C$ to use for $\angle R$. Then we draw lines for the two remaining sides $\overline{PQ}$ and $\overline{QR}$. The intersection of the two lines is the vertex $Q$ of triangle $\triangle PQR$.

Answer:

A. Copy $\overline{BC}$ from $\triangle ABC$ to form $\overline{PR}$. Then copy $\angle B$ to use for $\angle P$ and copy $\angle C$ to use for $\angle R$. Draw lines for the two remaining sides $\overline{PQ}$ and $\overline{QR}$. The intersection of the two lines is the vertex $Q$ of triangle $\triangle PQR$