ct 1314 1516 Which lines can you conclude are parallel given

ct 13/14 15/16 Which lines can you conclude are parallel given that m27 + m211 - 180? Justify your conclusion with a theorem. Line a is parallel to line b by the Converse of the Same-Side Interior Angles Theorem. Line a is parallel to line b by the Converse of the Alternate Interior Angles Theorem. Line c is parallel to line d by the Converse of the Alternate Interior Angles Theorem. Line c is parallel to line d by the Converse of the Same-Side Interior Angles Theorem.

Solution

Hi,

We can conclude \" the line \'a\' is parallel to the line \' b\', by the converse of the same -side interior angles theorem.

We can justify the above with the following.

We have the statement of converse of same -side interior angle theorem ---\" if two lines( say \'a\' and \' b\' )are cut by a transversal ( here \'d\') and the same side interior angles { here m(7),M(11)} are supplementary here it is given[ M(7)+M(11)=180 given].then they are parallel.so here \'a\' and \'b\' are parallel, \' d\' is transversal.so from the theorem - converse of same side interior angle - we can justify that.

HOPE YOU LIKE THIS