## Task 2 – Drawing Similar Triangles (Part 2)

In the applet below, $A'B' = 2AB$, $A'C'= 2AC$, and $B'C'= 2BC$. Use the Segment tool to draw $\triangle PQR$ such that $PQ = 3AB$, $PR= 3AC$, and $QR = 3BC$.

Questions

1.) How did you draw ∆PQR?

2.) What do you observe about the corresponding angles of the ∆ABC, ∆A’B’C’ and ∆PQR?

Discussion

In Task 1 and Task 2, you have observed that it is easier to draw similar triangles if you make the corresponding sides of the triangles parallel. In addition, you have also observed that the corresponding angles of the triangles are congruent. For example,

$\angle A \cong \angle A'$

$\angle B \cong \angle B'$

and

$\angle C \cong \angle C'$

In drawing the triangles, you made sure that the ratio of the lengths of corresponding sides is equal. In other words, you made the length of the corresponding sides proportional. For instance, the ratio of the lengths of the corresponding sides of to those of is 2. That is,

$\frac{A'B'}{AB'} = 2$

$\frac{A'C'}{AC'} = 2$

$\frac{B'C'}{BC} = 2$

Two triangles whose corresponding angles are congruent are called similar triangles. The lengths of the corresponding sides of similar triangles are proportional.

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## Task 1 – Drawing Similar Triangles (Part 1)

In the applet below, given $\triangle ABC$, use the Segment tool to draw $\triangle A'B'C'$  such that $A'B' = 2AB$, $A'B' = 2AC$, and $B'C' = 2BC$.

Questions

1.) How did you draw $\triangle A'B'C'$?

2.) What do you observe about the angles of the two triangles?

3.) Draw other triangles satisfying the same conditions and see if your observations still hold.

In your lesson on Triangle Congruence, you have learned about corresponding angles and corresponding sides. In the two triangles above, the pairs of corresponding angles are $A$ and $A'$, $B$ and $B'$, and $C$ and $C'$. The pairs of corresponding sides are $AB$ and $A'B'$, $BC$ and $B'C'$ and $AC$ and $A'C'$.