Triangle Congruence - Explorations (two sides, one angle)In the following applet, you can move around and rotate the angles and line segments by grabbing points. Grabbing the red segment in the angle will move the angle. Look at this picture if you need a visual hint. Question 1. In the applet, you have two pairs of congruent sides and one pair of congruent angles. Are these two sides and angle enough to ensure the congruence of triangles constructed from these objects? In other words, can you create two different triangles, or will you be getting the same triangles no matter how you arrange the sides/angle? Question 2. Now think about a stronger condition: You are allowed to create only triangles that have the given angle included between the two sides. Can you create two different triangles? Question 3. Now let's make the condition a bit weaker. You do not have to include the angle between the two sides, but you have to make sure, that a pair of corresponding angles are congruent; for example if you make the 25-degree angle adjacent to the line segment with the lenght 3 in one triangle, it must be adjacent to the line segment with the lenght 3 in the other triangle (and the other way around; if it is opposite in one, it must be opposite in the other). Can you create two different triangles? Question 4. (bonus question not discussed in the class) Now try to create triangles so that the angles opposite the longer side are congruent. Can you create two different triangles? Tibor Marcinek, Created with GeoGebra |