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In triangle ABC the sides BA and CA have been produced such that BA=AP and CA=AE prove that DE parallel to BC. plz it's urgent |
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Answer» Step-by-step explanation:In order to PROVE that DE∥BC it is sufficient to prove that either ∠CED=∠ECB or ∠BDE=∠DBC. For this, let us consider the triangles EAD and CAB. In these TWO triangles, we have EA=AC [Given] AD=AB [Given] ∠EAD=∠BAC [Vertically OPPOSITE angles] So, by SAS congruence CRITERION, we obtain ΔEAD≅ΔCAB ⇒∠AED=∠ACB and ∠ADE=∠ABC ⇒∠CED=∠ECB and ∠BDE=∠ABC Hence, DE∥BC |
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