Question

lab 4.2: constructing congruent triangles - sss, sas, and asa postulates
in this construction, you will use the side - side - side postulate to construct a triangle congruent to a given triangle. ask your teacher for help.
construction 4a: construct triangle △rst congruent to △abc using the sss postulate.
tools needed: compass, straightedge, pencil
step 1: draw ℓ longer than (overline{ab}). pick a point on ℓ and label it r.
step 2: place your compass point at a on △abc and draw an arc that passes through b.
step 3: without changing your compass width, place your compass point on r and draw an arc that intersects ℓ. label this point s.
step 4: now place your compass point at a again and draw an arc that passes through c.

Explanation:

Step1: Draw a ray

Draw a ray $\ell$ longer than side $AB$ of $\triangle ABC$ and pick a point $R$ on it. This gives us a starting - point for constructing the new triangle.

Step2: Copy side $AB$

Place the compass point at $A$ on $\triangle ABC$ and draw an arc that passes through $B$. Then, without changing the compass width, place the compass point at $R$ on $\ell$ and draw an arc that intersects $\ell$. Label this point $S$. So, $RS = AB$.

Step3: Copy side $AC$

Place the compass point at $A$ again and draw an arc that passes through $C$.

Step4: Find the third vertex

Without changing the compass width, place the compass point at $R$ and draw an arc. Then, place the compass point at $S$ and draw an arc with the length of $BC$ (by first measuring $BC$ with the compass from $\triangle ABC$). The intersection of these two arcs is point $T$. $\triangle RST$ is congruent to $\triangle ABC$ by the SSS (Side - Side - Side) postulate.

Answer:

A triangle $\triangle RST$ congruent to $\triangle ABC$ is constructed using the steps above with the SSS postulate.