Congruent Triangles std8 Page-35.5 EM

Isosceles Triangle | One angle is 70° | Find the other angles

🔷 Isosceles Triangle ABC (AB = AC) 📐 Given: ∠A = 70° ❓ Find the other two angles (two possible cases)

✍️ Step-by-Step: Find all possible angles

1 Isosceles Triangle Property

In an isosceles triangle with AB = AC, which angles are equal?

2 Angle Sum Property

What is the sum of all three angles in any triangle?

3 Case 1: Given angle is the vertex angle

If ∠A = 70° is the vertex angle (between the equal sides), then ∠B = ∠C = ?

4 Calculate base angles for Case 1

(180° - 70°) / 2 = ?

5 Case 2: Given angle is a base angle

If ∠B = 70° is a base angle, then ∠C = ∠B = 70°. Then ∠A = ?

6 Calculate vertex angle for Case 2

180° - (70° + 70°) = ?

7 Case 3: Given angle could also be the other base angle

If ∠C = 70° is a base angle, the result is the same as Case 2. The angles are:

8 Possible sets of angles

What are the two possible sets of angles for the triangle?

9 Verification - Case 1 sum

Check Case 1: 70° + 55° + 55° = ?

10 Verification - Case 2 sum

Check Case 2: 40° + 70° + 70° = ?

📐 Isosceles Triangle | One angle is 70°