Month: June 2018

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.

Questions

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

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.