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Triangles

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10th class > Triangles > Summary

Summary

In this chapter you have studied the following points :

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

2. All the congruent figures are but the converse is not true.

3. Two polygons of the same number of sides are similar, if (i) their corresponding angles are and (ii) their corresponding sides are in the same ratio (i.e., proportion).

4. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the ratio.

5. If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the side.

6. If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are (AAA similarity criterion).

7. If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are (AA similarity criterion).

Note:

If in two right triangles, hypotenuse and one side of one triangle are proportional to the hypotenuse and one side of the other triangle, then the two triangles are similar. This may be referred to as the RHS Similarity Criterion.