5.2: Congruent Triangles
This activity is intended to supplement Geometry, Chapter 4, Lesson 4.
In this activity, you will explore:
- Conditions that create congruent triangles.
Use this document to record your answers.
Problem 1 – Three Corresponding Sides (SSS)
1. Based on your observations, are two triangles with three pairs of corresponding congruent sides (SSS) congruent?
2. Does this result change when a vertex of the triangle is dragged?
3. When the two compass circles are created, there are two points of intersection. Do you think it makes a difference which one you choose to be point ?
Problem 2 – Two Corresponding Sides and the Included Angle (SAS)
4. Based on your observations, are two triangles with two pairs of corresponding congruent sides and the included angle (SAS) congruent?
5. Do you think it matters whether the included angle is acute, right, or obtuse?
Problem 3 – Two Corresponding Angles and the Included Side (ASA)
6. Based on your observations, are two triangles with two pairs of corresponding congruent angles and the included side (ASA) congruent?
7. Why do you think the selection order of the angle vertices matters?
Apply The Math
Name the congruence postulate (SSS, SAS, or ASA) that shows the triangles to be congruent.
Extension – Two Corresponding Sides and the NON-Included Angle
Use the file you saved as CongTri. Investigate the results if you copy two sides of a triangle and the NON-included angle. Will the triangles be congruent?