Congruent Triangles std8 Page-28.2 EM

📐 Quadrilateral ABCD | Is it a Parallelogram?

AB = 4 cm, CD = 4 cm | ∠CAB = 35°, ∠ACD = 35° | Diagonal AC in green

🔵 Quadrilateral ABCD (sides in blue) 📏 AB = 4 cm, CD = 4 cm 🟢 Diagonal AC (green) 📐 ∠CAB = 35°, ∠ACD = 35°

✍️ Analyze Quadrilateral ABCD

1 Given Information

What are the given side lengths?

2 Given Angles

Which angles are given as equal?

3 Diagonal AC

What does the diagonal AC do to the quadrilateral?

4 Triangles formed by diagonal

Which two triangles are formed by diagonal AC?

5 Equal sides in triangles

What can we say about AB and CD?

6 Angles in triangles

In ΔABC and ΔCDA, which angles are equal?

7 Are the triangles congruent?

Are ΔABC and ΔCDA congruent? If yes, by which criterion?

8 Corresponding sides

From the congruence, what can we say about BC and DA?

9 Condition for parallelogram

What is a sufficient condition for a quadrilateral to be a parallelogram?

10 Final conclusion

Is quadrilateral ABCD a parallelogram? Why?