The following applet shows [math]\Delta ABC[/math] and [math]\Delta DEF[/math]. [br]Move points A, B, C, D, and E to change the orientation and size of the triangles.
Move points A, B, C, D, and E to change the triangles. Do the triangles appear similar?
[math]\triangle ABC[/math] and [math]\triangle DEF[/math] appear to be similar, but we cannot be sure.
Click to show the angles. What do you notice is always true?
[math]\angle A\cong\angle D[/math] and [math]\angle B\cong\angle E[/math]
What could you say about [math]\angle C[/math] and [math]\angle F[/math]?
They must also be congruent. [math]\left(\angle C\cong\angle F\right)[/math]
Click to show the side lengths. What do you notice about the sides?
The corresponding sides are in proportion, which makes the triangles similar. [math]\left(\triangle ABC\sim\triangle DEF\right)[/math]
Are your triangles congruent? If not, can you make them congruent?
Matching the lengths of side AB and side DE (using the slider) will make the scale factor 1:1. This makes the triangles [b]congruent.[/b] [math]\left(\triangle ABC\cong\triangle DEF\right)[/math]