gU5L2C: ∆ Cong. Criteria Part 3
There are two triangles in this applet. The triangles have the same angle measures. Click on the bottom right blue dot to resize one of the triangles.
1) Is it possible to two different triangles that have the same angles but different sides?
2) Can the AAA Criteria be used to prove congruent triangles?
Click Proof (or SLIDE) for the animation
3) What transformations are used to map one triangle to another triangle in the above activity?
4) Therefore, two triangles with the same sides will always be congruent.
Slide the bar to watch the animation and transformations
5) What transformations are observed in the above activity ?
6) Therefore, two triangles with the same 2 sides and same included angle (SAS) will always be congruent.
SSA Criteria Part A: Slide the bar to watch the animation and transformations
SSA Criteria Part B: Slide the bar for the animations. Then, determine if the triangle on the right can be mapped on to the left one. (One vertex will rotate it while the other will move it ).
7) If two triangles have the same SSA conditions, then one triangle CAN ALWAYS be mapped onto the other using rigid motions only.
Slide the bar to watch the animation. Map one triangle to the other (Blue dot will rotate while pink will move the triangles)
7) If 2 angles and the included side of one triangle are fixed, which of these is TRUE?
Use a series of transformations to map the triangle on the right to the one on the left. (One white vertex will move the triangle and the other will rotate it)
8) Therefore, are the triangles above congruent?
Take a minute to interact with this activity. Be very observant. Then, answer the two questions that follow.
9) If 2 angles of a triangle are congruent to 2 angles of another triangle, what can we conclude about the third pair of angles?
10) Therefore, the Angle-Angle-Side Triangle Congruence Theorem should be no surprise to us. Which other triangle congruence theorem is disguised here?
Use a series of rigid motions to map the triangle on the right to the one on the left. (One white vertex will allow you move it, the other will rotate it)
11) Therefore, are the triangles above congruent?
12) What have you learned in this, and yesterday's lesson regarding triangle congruence criteria. (State at least two ideas)