Congruent Triangles std8 Page-24.1.2 EM

Two Triangles | Find Equal Sides | ASA Congruence

△ LMN

∠L = 30° ∠M = 80° ∠N = 70°

△ XYZ

∠X = 70° ∠Y = 30° ∠Z = 80°

🔍 ASA Congruence Criterion: Two angles and the included side are equal 📐 Triangles are congruent → corresponding sides are equal

✍️ Find the equal sides of the two triangles

1 Third angle of ΔLMN

In ΔLMN, ∠L = 30°, ∠M = 80°. Find ∠N.

2 Third angle of ΔXYZ

In ΔXYZ, ∠X = 70°, ∠Y = 30°. Find ∠Z.

3 Identify equal angles

Which angles are equal in both triangles?

4 Included side in ΔLMN

In ΔLMN, the side between ∠L (30°) and ∠M (80°) is LM. But we are given LN. Which side is between ∠L and ∠N?

5 Included side in ΔXYZ

In ΔXYZ, which side is between ∠X (70°) and ∠Z (80°)?

6 Identify the correspondence

Looking at the angles, we see ∠L = 30° = ∠Y, ∠M = 80° = ∠Z, ∠N = 70° = ∠X. What is the correct correspondence?

7 Side equal to LN

In ΔLMN, LN is between ∠L (30°) and ∠N (70°). Which side of ΔXYZ is between ∠Y (30°) and ∠X (70°)?

8 Length of XY

What is the length of XY? (Given)

9 Side equal to LM

LM is between ∠L (30°) and ∠M (80°). Which side of ΔXYZ is between ∠Y (30°) and ∠Z (80°)?

10 Side equal to MN

MN is opposite ∠L (30°). Which side of ΔXYZ is opposite ∠Y (30°)?

📐 Two Triangles | Find Equal Sides