Two triangles are congruent if their corresponding sides and angles are congruent. That’s the definition. But you do not need to satisfy all these six pairs of congruences before you can make the conclusion that indeed two triangles are congruent.
Finding the minimum conditions to determine if two triangles is a good investigation activity in geometry. In investigating for the minimum condition for triangle congruence, you can start with SSS Congruence. You can then ask the students to find out the rest of the combinations. However if you feel that the students need some guide in constructing the angles, you can start with the ASA combination. You can try the procedure using the applet below. There is also a student version of the ASA worksheet. Click link to open then save it. Challenge the students to determine if the order of the two angles and the other side matter. That is, can it be any two angles and any one of the three sides?
- Construct angle <D> congruent to angle A. To do this select a point on AB then use the Compass tool to draw Circle D and then Circle A.
- Use the intersection tool to construct the point of intersection between Circle D and line t and Circle A and AC.
- Construct Circle <H> with radius FG.
- Use the Intersection tool to construct the intersection between of Circles D and H then draw a ray through this intersection and point D using the Ray tool.
- Construct angle E congruent to angle C. Identify the intersection point the draw th triangle using the POLYGON tool.
You can check the construction using the FORWARD or PLAY button. Click REFRESH button to repeat or make your own construction.