Question

1. triangle abc is shown below. construct △rst such that △rst≅△abc. properly label the vertices of △rst. leave all construction marks.

Explanation:

Step1: Draw a line segment

Draw a line segment of length equal to one of the sides of $\triangle ABC$, say $RS = AB$. Use a straight - edge to draw a line and mark points $R$ and $S$ on it such that the distance between them is equal to the length of $AB$ measured with a compass.

Step2: Copy an angle

Place the compass at point $A$ of $\triangle ABC$ and draw an arc that intersects $AB$ and $AC$ at two points. Without changing the compass width, place the compass at point $R$ and draw a similar arc. Then, measure the angle at $A$ using the compass by placing the compass on the intersection points of the arc and the sides of $\angle A$ and transfer this angle to point $R$ of the new line segment $RS$. Let the new ray be $RX$.

Step3: Determine the third vertex

Measure the length of $AC$ with the compass. Place the compass at point $R$ and draw an arc on the ray $RX$ with a radius equal to the length of $AC$. Mark the intersection point as $T$.

Step4: Complete the triangle

Connect points $S$ and $T$ with a straight - edge to form $\triangle RST$. By the Side - Angle - Side (SAS) congruence criterion, $\triangle RST\cong\triangle ABC$.

Answer:

The constructed $\triangle RST$ with vertices $R$, $S$, and $T$ such that $\triangle RST\cong\triangle ABC$ is as described in the steps above. (Note: In an actual construction, the construction marks like arcs should be left as required by the problem statement).