Math Activity: Proving the SAS Congruence theorem

This activity is based on Tanzanian Mathematics Syllabus for Secondary Schools. As a student, you are supposed to perform a series of tasks to develop an understanding of congruence of figures as well as proving the SAS congruence theorem. Proceed as follows: 

1. You are provided with shapes of different size as those shown in the figure below. Use any means of       your choice, sort out figures which are exactly the same. Give reasons. 

    
   

2.     For the group of same figures, take two sets of figures and measure their angles and sides and draw a conclusion about your observation.

3.     Repeat task 3 but this time, use one figure from each group. What is your observation?

4.     Based on findings in tasks 3 and 4, what properties make the figures same or different?

5.     What is the term used to describe figures which are exactly the same? What are common properties of such figures?

6.     Use different math resources such as books and internet to confirm your results. 

7.     Use the online interactive exercise by clicking here to test your understanding of the congruence of figures. 

8.      One of the methods of proving if two triangles are congruent is by checking if two pairs of corresponding sides of the triangles are equal and a pair of angles formed by the sides are equal. Study the following figure to learn how to identify the pair of equal sides and the included angle. Make a summary of what you have learned to demonstrate your understanding. 

9.     Take two cards from a set of congruent triangles and indicate corresponding equal sides and included angle. Show the actual lengths and angles. Check if all congruent figures have same property.


Source: Math is Fun

    10. Take two cards from a set of congruent triangles and indicate corresponding equal sides        and included angle. Show the actual lengths and angles. Check if all  congruent figures         have same property.        

11. Draw three sets of congruent triangles with the properties you have learned in task 10.

12. Based on findings in tasks 10 and 11, why you may be confident to confirm if two triangles are congruent by using these conditions?

13. Study the following example to learn more on how to prove congruence of triangles by SAS theorem.

    12. Practice the SAS theorem by attempting the questions in the following worksheet


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