SAS Congruency (Measuring Two Sides and the Included Angle)

Transcript

SAS Congruency (Measuring Two Sides and the Included Angle)Now, we are given this situation ∆ABC and ∆XYZ are two triangles such that AB = XY = 6 cm, AC = XZ = 5 cm, and ∠A = ∠X = 30°. Are they congruent? Let’s first draw the diagram Let’s try to Construct this triangle We follow the same method we used in Chapter 7 Class 7 – A tale of 3 intersecting lines (Ganita Prakash Book 1) We notice that from these measurements We can create only one type of triangle. So, all triangles with these measurements are congruent Thus, we can conclude When two sides and the included angle of two triangles are equal, the two triangles are congruent. This is referred to as the SAS (Side Angle Side) condition for congruence.