Congruent Triangles std8 Page-35.6 EM

Isosceles Triangles | 70° angle and 8 cm side | All Possible Triangles

🔷 Isosceles triangle (two equal sides) 📐 One angle = 70° 📏 One side = 8 cm ❓ How many non-congruent triangles?

✍️ Step-by-Step: Find all possible triangles

1 Given angle possibilities

The 70° angle could be which type of angle in the isosceles triangle?

2 Case 1: 70° is the vertex angle

If 70° is the vertex angle, what are the base angles?

3 Given side possibilities in Case 1

In Case 1, the 8 cm side could be:

4 Case 1A: 8 cm is the equal side

If the equal sides are 8 cm each, what is the base length? (Using Law of Cosines)

5 Case 1B: 8 cm is the base

If the base is 8 cm, what is the length of the equal sides? (Using Law of Cosines)

6 Case 2: 70° is a base angle

If 70° is a base angle, what is the vertex angle?

7 Given side possibilities in Case 2

In Case 2, the 8 cm side could be:

8 Case 2A: 8 cm is the equal side

If the equal sides are 8 cm each, what is the base length?

9 Case 2B: 8 cm is the base

If the base is 8 cm, what is the length of the equal sides?

10 Total number of non-congruent triangles

How many non-congruent isosceles triangles satisfy the conditions?

📐 Isosceles Triangles | 70° angle and 8 cm side