Triangles: Important Points You must Know

1. Two figures are said to be similar if and only if they have same shape but not necessarily of same size.
2. All the congruent figures are similar but the converse is not true.
3. Two polygons of the same number of sides are similar if and only if
(i) their corresponding angles are equal
(ii) their corresponding sides are in proportion (same ratio).
4. Basic Proportionality Theorem (Thales Theorem):
5. Converse of Basic Proportionality Theorem: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to third side.
6. Similar Triangles: Two triangles are similar if and only if
i. their corresponding angles are equal i.e. they are equi-angular and
ii. their corresponding sides are in the same ratio.
7. Criteria for establishing similarity of two triangles:
i. AA (or AAA) criterion of similarity
ii. SSS criterion
iii. SAS criterion
iv. Altitude of right angle triangles
2. All the congruent figures are similar but the converse is not true.
3. Two polygons of the same number of sides are similar if and only if
(i) their corresponding angles are equal
(ii) their corresponding sides are in proportion (same ratio).
4. Basic Proportionality Theorem (Thales Theorem):
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 same ratio.(see figure above)
5. Converse of Basic Proportionality Theorem: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to third side.
6. Similar Triangles: Two triangles are similar if and only if
i. their corresponding angles are equal i.e. they are equi-angular and
ii. their corresponding sides are in the same ratio.
7. Criteria for establishing similarity of two triangles:
i. AA (or AAA) criterion of similarity
ii. SSS criterion
iii. SAS criterion
iv. Altitude of right angle triangles