Some of the basic you have to learn first they are….

1. Ratio of the area of two triangles.
2. Basic proportionality theorem.
3. Theorem of an angle bisector of a triangle.
4. Similarity of triangles
5. Theorem of area of similar triangle.

1. Ratio of areas of two triangles.

Statement: Ratio of two triangles is equal to the ratio of the product of their bases and corresponding height.

Example :

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2. Basic proportionality theorem.

Statement: If a line parallel to a side of a triangle,interests the remaining sides in two distinct point, then the line divides the sides in the same proportion.

Example: let a triangle ABC and segment DE intersects at two remaining side of triangle then the divided line AB and line AC is in same proportion.

3.Theorem of an angle bisector of a triangle.

Statement: The bisector of an angle of a triangle divided the side opposite to the angle in the ratio of the remaining sides.

Example:

4. Similarity of triangles.

Let us first know about similar figures.

• Similar figures are always of same shape but can be different in sizes.
• Congruent figures are the similar figures of same shape and size

Similar triangles: one to one correspondence between the vertices of two triangles,

If,

• Their corresponding angles are congruent.
• Sides are same proportion, then the correspondence is known as similarity and then two triangles are know to be similar triangles.

There are three tests of similarity of triangles.

1. AAA test or (AA test)
2. SAS test
3. SSS test

5.Theorem of area of similar triangle.

Statement: Two triangles are similar, the ratio of areas of those triangles is equal to the ratio of the square of their corresponding sides.