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Triangles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsTriangles1 Mark
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Answer

Given : l || m and p || q
To prove : DABC $\cong$ DCDA
Proof : l || m and p || q . . . . [Given]
In DABC and DCDA
$\angle$BAC = $\angle$DCA . . . . . [Alternate interior angles as AB || DC]
Similarly, $\angle$ACB = $\angle$CAD . . . [Alternate interior angles as BC || DA]
AC = DA . . . [Common]
DABC $\cong$ DCDA    [By ASA congruency]

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