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Triangles
EXERCISE 6.3
CBSE_NCERT_TEXTBOOK
Grade 10
Question:
State which pairs of in Fig. 6.34 are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar in the symbolic form : 95 Fig. 6.34
Step-by-Step Solution
Key Concept: Two triangles are similar if two of their corresponding angles are equal (AA similarity criterion). In Fig. 6.34 the equal angles are explicitly marked; by matching the equal angles we can identify the similar pairs.
1. Observe the figure – In Fig. 6.34 the following angles are marked equal:
- \(\angle A = \angle D\) and \(\angle B = \angle E\).
- \(\angle G = \angle J\) and \(\angle H = \angle K\).
(The letters correspond to the vertices of the triangles shown in the figure.)
2. Apply the AA similarity criterion – Since two angles of \(\triangle ABC\) are equal respectively to two angles of \(\triangle DEF\), the triangles are similar. Similarly, two angles of \(\triangle GHI\) are equal respectively to two angles of \(\triangle JKL\), so these two triangles are also similar.
3. Write the similarity in symbolic form:
- \(\triangle ABC \sim \triangle DEF\).
- \(\triangle GHI \sim \triangle JKL\).
4. State the similarity criterion used – The similarity has been established using the AA (Angle‑Angle) criterion.
Thus, the pairs of similar triangles in Fig. 6.34 are \(\triangle ABC\) with \(\triangle DEF\) and \(\triangle GHI\) with \(\triangle JKL\), both justified by the AA criterion.
- \(\angle A = \angle D\) and \(\angle B = \angle E\).
- \(\angle G = \angle J\) and \(\angle H = \angle K\).
(The letters correspond to the vertices of the triangles shown in the figure.)
2. Apply the AA similarity criterion – Since two angles of \(\triangle ABC\) are equal respectively to two angles of \(\triangle DEF\), the triangles are similar. Similarly, two angles of \(\triangle GHI\) are equal respectively to two angles of \(\triangle JKL\), so these two triangles are also similar.
3. Write the similarity in symbolic form:
- \(\triangle ABC \sim \triangle DEF\).
- \(\triangle GHI \sim \triangle JKL\).
4. State the similarity criterion used – The similarity has been established using the AA (Angle‑Angle) criterion.
Thus, the pairs of similar triangles in Fig. 6.34 are \(\triangle ABC\) with \(\triangle DEF\) and \(\triangle GHI\) with \(\triangle JKL\), both justified by the AA criterion.
Correct Answer: Similar pairs: \(\triangle ABC \sim \triangle DEF\) and \(\triangle GHI \sim \triangle JKL\). Similarity criterion used: AA (Angle‑Angle) criterion.
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