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Mathematics · Triangles · NCERT Examples

Example 4

A complete, independently verified solution for NCERT Example 4.

Mathematics · Chapter 6 · NCERT Examples

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NCERT Example

Example 4

AAA similarity · parallel lines

In Figure 6.29, PQ ∥ RS. Prove that △POQ ∼ △SOR.

Lines PS and QR are parallel and diagonals PR and QS intersect at O.
Figure 6-29 from the supplied NCERT chapter.

Solution

Board-exam working:

Given: PQ ∥ RS.

∠OPQ = ∠OSR because they are alternate interior angles.

∠OQP = ∠ORS because they are alternate interior angles.

Also, ∠POQ = ∠SOR because they are 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.