Question

in the given figure ab parallel CD and EF parallel CD prove that angle BAE equal angle DCE​

Answer 1

Answer:

Step-by-step explanation:

e are given the figure in the question in which AB║CD.

Firstly, we will make some construction in the figure such that;

Draw a line EF through point E which is parallel to the line AB and CD.

This means EF║AB ║CD.

Since EF║AB and AE act as a transversal, this means that;

AEF and BAE are supplementary because the sum of co-interior angles is 180°, i.e;

AEF + BAE = 180°  

AEF = 180° -  BAE     ----------------- [Equation 1]

Similarly, EF║CD and CE act as a transversal, this means that;

CEF and DCE are supplementary because the sum of co-interior angles is 180°, i.e;

CEF + DCE = 180°   ----------------- [Equation 2]

Now, from the diagram it is clear that CEF can be written as a sum of AEF and AEC, that means;

CEF + DCE = 180°  

(AEF +  AEC) + DCE = 180°  

180° -  BAE +  AEC + DCE = 180°    {using equation 1}

   BAE -  DCE =  AEC    {Hence Proved}