Ex.7.1 Q4 Triangles Solution - NCERT Maths Class 9


\(l\) and \(m\) are two parallel lines intersected by another pair of parallel lines \(p\) and \(q\) (see the given figure). Show that \(\Delta ABC \cong \Delta CDA\).

 Video Solution
Ex 7.1 | Question 4

Text Solution

What is Known?

\(l\parallel m\,\,\,and\,\,\,\,p\parallel q\,\)

To prove:

\(\Delta {\text{ABC}} \cong \Delta {\text{CDA}}{\text{.}}\)


We can show both the triangles congruent by using ASA congruency criterion


In \(\Delta ABC\) and \(\Delta CDA\),

\(\begin{align}&\angle BAC \,\text{and}\, \angle DCA \\&\text{(Alternate interior angles, as}(p \|q)\\\\AC &= CA \text{(Common)}\\&\angle BAC  \text{and} \angle DCA \\&\text{(Alternate interior angles, as} (l \|m)\\\\&\therefore\,\, \Delta ABC \cong \Delta CDA \\&\text{(By ASA congruence rule)}\end{align}\)

 Video Solution
Ex 7.1 | Question 4
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