SSA Congruency (Measuring Two Sides and a Non-included Angle)

Transcript

SSA Congruency (Measuring Two Sides and a Non-included Angle)We try triangles where two sides and a non-included angle are equal. Our situation now is ∆ABC and ∆XYZ are two triangles such that AB = XY = 6 cm, AC = XZ = 4 cm, and ∠B = ∠Y = 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) Steps of construction 1. Draw a line segment BA of length 6 cm 2. Now, using protractor, we draw 30° from point B 3. Since AC = 3 cm. Taking A as center, 3 cm as radius, we draw an arc 4. The arc intersects the ray from point B at two points. Let’s call them point C and D 5. Mark both triangles and label Thus, we have two possible triangles ∆ ABC and ∆ ABD So, from our construction we get two possible triangles ∆ ABC & ∆ ABD And, these triangles are not congruent This is called the SSA (Side Side Angle) condition. So, we can conclude that We have seen that SSA condition does not guarantee congruence