# Ex.7.1 Q4 Triangles Solution - NCERT Maths Class 9

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## Question

\(l\) 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

Triangles

Ex 7.1 | Question 4

## Text Solution

**What is Known?**

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

**To prove:**

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

**Reasoning:**

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

**Steps:**

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

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