Question

mathematics ch 5 ex 5.2 question 1 class 7​

Answer 1

$\mathbb {QUESTION} \\ \sf 1 . State \: the \: property \: that \: is \: used \: in \: each \: of \: the \: following \: statements \: ? \\ \sf \: ( i ) - If \: a || b, \: then \: ∆1 = ∆5 . \\ \sf \: ( ii ) - If \: ∆4 = ∆6, \: then \: a || b . \\ \sf \: ( iii ) - If \: ∆4 + ∆5 = 180°, \: then \: a || b . </p><p></p><p>[tex] \sf ( \:Explanation \: ) - Proof \: of \: ∆1 = ∆5 \\ \\ \sf \: </p><p></p><p>Here \: a || b \: ∆1 \: and \: ∆5 \: are \: corresponding \: angles. \: The \: corresponding \: angles \: are \: equal. \\ \\ \sf</p><p></p><p> Hence , ∆1 = ∆5 \\ \\ \sf ( \: Final Answer \: ) \\ \\ </p><p></p><p> \sf If \: a || b, \: then \: ∆1 = ∆5 \: are \: corresponding \: angle \: property . \: \\ \\ </p><p></p><p> \sf ( \: ii ) - If \: ∆4 = ∆6, \: then \: a || b . \\ \\ \sf ( \:Explanation \: ) -Proof \: of \: a || b \\ \\ </p><p></p><p>\sf \: we \: know \: that \: if \: the \: alternate \: interior \: angles \: are \: equal \: then \: the \: lines \: are \: parallel . \\ \\ </p><p></p><p>\sf \: Hence , \: ∆4 = ∆6 \: are \: two \: alternative \: interior \: angles . \: \\ \\ \: \sf \: ( iii ) - If \: ∆4 + ∆5 = 180°, \: then \: a || b . </p><p></p><p>Hence, a || b \\ \\ \sf \: ( \:Explanation \: ) -Proof \: of \: a || b , \\ \\ </p><p></p><p> \sf \: we \: know \: that , \: if \: the \: sum \: of \: interior \: angles \: of \: the \: same \: side \: of \: the \: transversal \: lines \: are \: equal . \\ \\ \sf</p><p></p><p>Here , \: ∆4 + ∆5 = 180° . Hence, \: a || b . </p><p></p><p></p><p></p><p>$