```E Board: Suggested Books     ICSE Board:  Foundation Mathematics
Class 8: Reference Books     Class 8: NTSE Preparation
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Theorem 1: If two sides of the triangles are equal, then the opposite angles are equal.

In the given diagram, if $AB=AC, \ then\ \angle ABC = \angle ACB$

Theorem 2: If the two angles of a triangle are equal in measure, then the sides opposite to them are equal.

In the given diagram, if $\angle ABC=\angle ACB, \ then \ AB=AC$

Results on Inequalities

Theorem 1: The sum of any two sides of a triangle is always greater than the third side.

Theorem 2: The difference of any two sides of a triangle is less than the third side.

Theorem 3: If two sides of a triangle are of unequal lengths, then the greater side has the greater angle opposite to it. It is easier to see that in the following diagrams.

In Figure 1, $BC$ is clearly the longest side and it is visibly clearly that $\angle A > \angle B \ and\ \angle A> \angle C$.

In Figure 2,$AB$ is the longest side. The visual representation makes it very clear that $\angle C > \angle B \ and\ \angle C> \angle A$.

Theorem 4: This is the converse of the above Theorem. If two angles of a triangle are of unequal measures, then the greater angle would have the greater side opposite to it. Similarly, if we look at the above two figures, we can also infer the converse.  In Figure 1,$\angle A > \angle B \ and\ \angle A> \angle C$ and hence $BC$ is the longest side. In Figure 2, $\angle C > \angle B \ and\ \angle C> \angle A$ and hence $AB$ is the longest side.

```E Board: Suggested Books     ICSE Board:  Foundation Mathematics
Class 8: Reference Books     Class 8: NTSE Preparation
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