‘रचना-प्रयोग’ का मुख्य उद्देश्य क्या है?

व्याकरण का व्यावहारिक प्रयोग सिखाना

‘द्वितीयः’ किस प्रकार की संख्या है?

क्रमवाचक (दूसरा)

State the Basic Proportionality Theorem (Thales’ theorem).

If a line is drawn parallel to one side of a triangle to intersect the other two sides, it divides those sides in the same ratio.

State the AA similarity criterion.

If two angles of one triangle are equal to two angles of another, the triangles are similar.

When are two triangles said to be similar?

When their corresponding angles are equal and their corresponding sides are in the same ratio (proportion).

State the Basic Proportionality Theorem (Thales’ theorem).

If a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct points, it divides those two sides in the same ratio (refer to the figure in your NCERT textbook).

Name the criteria used to prove two triangles similar.

The AA (or AAA), SSS and SAS similarity criteria.

State the AA similarity criterion.

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

How are the areas of two similar triangles related to their sides?

The ratio of the areas of two similar triangles equals the square of the ratio of any pair of corresponding sides.

In a triangle, a line parallel to BC meets AB at D and AC at E. If \(AD/DB = 3/4\), find \(AE/EC\).

By the Basic Proportionality Theorem, \(AE/EC = AD/DB = 3/4\).

If two similar triangles have corresponding sides in the ratio \(2 : 3\), what is the ratio of their areas?

The ratio of areas is the square of the ratio of sides, i.e. \(4 : 9\).

Give one real-life use of similar triangles.

Finding inaccessible heights and distances, such as the height of a tower or tree using the length of its shadow and a known object’s shadow.

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Chapter 6: TrianglesClass 10 Mathematics — summary, notes, extra questions & NCERT solutions

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Two figures having the same shape but not necessarily the same size are called:

Summary

This chapter studies similarity of triangles — figures of the same shape but not necessarily the same size. Two triangles are similar when their corresponding angles are equal and corresponding sides are in proportion. The Basic Proportionality Theorem (Thales’ theorem) states that a line parallel to one side of a triangle divides the other two sides in the same ratio. Criteria such as AA, SSS and SAS establish similarity, and similar triangles are used to prove results and find unknown lengths in geometric and real-life problems involving heights and shadows.

Similar figuresBasic Proportionality TheoremCriteria for similarity (AA, SSS, SAS)Applications of similar triangles

Key terms

Similar triangles

Triangles with equal corresponding angles and proportional sides.

Basic Proportionality Theorem

A line parallel to one side divides the other two sides proportionally.

AA criterion

Two triangles are similar if two pairs of angles are equal.

Corresponding sides

Sides opposite to equal angles in similar triangles.

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EXERCISE 6.1

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Triangles with equal corresponding angles and proportional sides.

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