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

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

**Questions**

1.) How did you draw ∆PQR?

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

3.) Based on **Task 1** and Task 2, make a conjecture about your observations above.

**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,

$latex \angle A \cong \angle A’$

$latex \angle B \cong \angle B’$

and

$latex \angle C \cong \angle C’$

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,

$latex \frac{A’B’}{AB’} = 2$

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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**Next: Task 3 of 5**