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Mathematics · Triangles · NCERT Examples

Example 5

A complete, independently verified solution for NCERT Example 5.

Mathematics · Chapter 6 · NCERT Examples

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NCERT Example

Example 5

SSS similarity · corresponding angles

Observe Figure 6.30 and find ∠P.

Triangles ABC and PQR with side lengths and angles marked for an SSS similarity calculation.
Figure 6-30 from the supplied NCERT chapter.

Solution

Board-exam working:

In △ABC and △RQP:

ABRQ=3.87.6=12\frac{AB}{RQ}=\frac{3.8}{7.6}=\frac12
BCQP=612=12\frac{BC}{QP}=\frac6{12}=\frac12
CAPR=3363=12\frac{CA}{PR}=\frac{3\sqrt3}{6\sqrt3}=\frac12

Thus:

ABRQ=BCQP=CAPR\frac{AB}{RQ}=\frac{BC}{QP}=\frac{CA}{PR}

Therefore, △ABC ∼ △RQP by SSS similarity.

The verified correspondence is A ↔ R, B ↔ Q and C ↔ P. Hence ∠P = ∠C.

By the angle-sum property, ∠C = 180° − 80° − 60° = 40°.

Final answer

∠P = 40°.