Question

we learned previously in this unit that a circle is simply the collection of all points that are a set distance away from a center point. likewise, an arc is a portion of a circle where all the points are the same distance away from a given point. we can use these facts, along with a protractor, to locate points and to copy triangles.
exercise #1: in the diagram below, segment $overline{ab}$ has a length of 3 inches, in other words $ab = 3$. point $c$ is above $overline{ab}$, is 2 inches from $a$, and is 1.5 inches from $b$. using the ruler below to set your compass length, locate point $c$ by drawing arcs along two circles. then draw $\triangle abc$.
exercise #2: using your ruler only to draw straight line segments, construct a triangle that has side lengths that are the same as the three segments shown below. leave all construction marks.
exercise #3: use tracing paper to compare your triangle with students sitting next to you. how do they compare? are they identical except for their location on the page?

Explanation:

Step1: Locate point C for Exercise #1

Set compass to 2 inches and place the compass - point at A to draw an arc. Then set the compass to 1.5 inches and place the compass - point at B to draw another arc. The intersection of the two arcs above $\overline{AB}$ is point C. Then draw $\triangle ABC$.

Step2: Construct triangle for Exercise #2

Let the three given line - segments be $a$, $b$, and $c$. First, draw a line - segment of length $a$. Then, using the compass, set the length to $b$ and with one end of the first line - segment as the center, draw an arc. Next, set the compass length to $c$ and with the other end of the first line - segment as the center, draw another arc. The intersection of the two arcs gives the third vertex of the triangle.

Step3: Compare triangles for Exercise #3

When using tracing paper to compare the triangles, if the side - lengths of the triangles are the same (constructed using the SSS (Side - Side - Side) congruence criterion), the triangles are congruent. They will be identical in shape and size, and the only difference may be their position on the page.

Answer:

For Exercise #1: $\triangle ABC$ is constructed with $AB = 3$ inches, $AC = 2$ inches, and $BC = 1.5$ inches.
For Exercise #2: A triangle is constructed with side - lengths equal to the three given line - segments.
For Exercise #3: If the side - lengths are the same, the triangles are congruent (identical in shape and size, differing only in position).