🔼Inequalities of a triangle,similarity,Midpoint theorem and Pythagoras theorem made easy with TLM ✍️

Описание: 🔼Inequalities of a triangle,similarity,Midpoint theorem and Pythagoras theorem made easy✨😇😄 with TLM

1. Inequalities of Triangles🔼

In a triangle, certain inequalities always hold true:

Sum of two sides is greater than the third side: For any triangle with sides ,
, , and .

Difference of two sides is less than the third side:
, , .
These inequalities ensure that three given lengths can actually form a triangle.

2. Similarity of Triangles

Two triangles are similar if they have the same shape but not necessarily the same size. This means:

Their corresponding angles are equal.

Their corresponding sides are in the same ratio.
Conditions for similarity:

AA (Angle–Angle): Two angles equal in each triangle.

SSS (Side–Side–Side): Ratios of all corresponding sides equal.

SAS (Side–Angle–Side): Ratio of two sides equal and included angle equal.

3. Midpoint Theorem

The Midpoint Theorem states:
The line segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
If and are midpoints of sides and in , then:

4. Pythagoras Theorem

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
If p and b are the Perpendicular and base and h is the hypotenuse then:

h²= p² + b²

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