Change resourceExample 4
Mathematics · Chapter 6 · NCERT Examples
Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.
In Figure 6.29, PQ ∥ RS. Prove that △POQ ∼ △SOR.
Figure 6-29 from the supplied NCERT chapter.Solution
Given:
PQ is parallel to RS, and the intersecting lines meet at O.
To prove:
Triangle POQ is similar to triangle SOR.
Figure 6-29 from the supplied NCERT chapter.Proof:
Alternate interior angles, since PQ is parallel to RS.
Alternate interior angles, since PQ is parallel to RS.
Vertically opposite angles.
Thus the correspondence is P ↔ S, O ↔ O and Q ↔ R.
Therefore, △POQ ∼ △SOR by the AAA similarity criterion.
Final answer
Therefore, △POQ ∼ △SOR.
