Question

given $\triangle abc$, describe how to construct $\triangle pqr$ congruent to $\triangle abc$ using each of the following combinations.
a. two sides of $\triangle abc$ and an angle included between these two sides
b. the three sides of $\triangle abc$
c. two angles and a side included between these angles
copy $angle c$ from $\triangle abc$ to form $angle p$. then copy sides $overline{ac}$ and $overline{bc}$ to form $overline{pq}$ and $overline{pr}$, respectively. draw the third side, $overline{qr}$, by connecting the ends of $overline{pq}$ and $overline{pr}$.
follow the steps to construct $\triangle pqr$. choose the correct answer below.

Explanation:

Step1: Analyze option A

In option A for the first - part (two sides and included angle), the orientation of the sides and angle is wrong compared to the construction requirements.

Step2: Analyze option B

For the case of two sides and the included angle, in option B, we first copy the included - angle. Then we copy the two sides adjacent to that angle in the correct order and orientation. This matches the Side - Angle - Side (SAS) congruence construction.

Step3: Analyze option C

Option C does not show the correct copying of sides and angles as per the given congruence criteria.

Step4: Analyze option D

Option D also has incorrect orientation and copying of sides and angles for the given congruence cases.

Answer:

B