Congruent Triangles std8 Page-18.4 EM

Kite ABCD | Triangles ADB and ADC | Angle Comparison

🔷 Kite ABCD: AB = AD = 4, BC = CD = 3 📐 Diagonal AC divides kite into △ADB and △ADC ❓ Do the two triangles have the same angles?

✍️ Compare Triangles ADB and ADC

1 Side lengths of △ADB

Triangle ADB has sides: AD = 4, AB = 4, and BD = ? (unknown). What type of triangle is ADB?

2 Side lengths of △ADC

Triangle ADC has sides: AD = 4, AC = ?, and DC = 3. What type of triangle is ADC?

3 Compare AD in both triangles

Is side AD equal in both triangles ADB and ADC?

4 Compare AB and DC

AB = 4, DC = 3. Are these equal?

5 Compare the third sides

BD (in △ADB) and AC (in △ADC) are: BD is the other diagonal, AC is the given diagonal.

6 Are the triangles congruent?

Do the two triangles have all three sides equal? (SSS condition)

7 Do they have the same angles?

If triangles are not congruent, do they still have the same angles?

8 Final conclusion

Do triangles ADB and ADC have the same angles? Why?

📐 Kite ABCD | Triangles ADB and ADC