@ In a triangle ABC, D is mid-point of BC; AD is produced upto E so that DE = AD. Prove that : (1) A ABD and A ECD are congruent. (ii) AB = EC. (iii) AB is parallel to EC. X 1 DO
Answers
Given:
A ΔABC in which D is the mid-point of BCAD is produced to E so that DE=AD
We need to prove that :
(i) ΔABD and ΔECD are congruent
(ii) AB = CE
(iii) AB is parallel to EC
In ΔABD and ΔECD
- BD=DC [ D is the midpoint of BC ]
- ADB=CDE [ vertically opposite angels ]
- AD=DE [ Given ]
∴ By Side-Angel-Side criterion of congruence, we have,
ΔABD ≅ ΔECD
(ii) The corresponding parts of the congruent triangles are congruent.
∴ AB=EC [ c.p.c.t ]
(iii) Also, DAB = DEC [ c.p.c t ]
AB || EC [ DAB and DEC are alternate angels ]
Answer:
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