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Angle Bisector Homework Help

In an arbitrary triangle, ABC we will draw and angle bisector from B towards AC and will name it as D. In simple words it means that the angle is bisecting or dividing a large triangle into two small triangles that is ABC, which is a large triangle and two small triangles are ABD and triangle CBD. In the Angle Bisector Theorem we will understand that the ratio between the two sides of the two triangles is going to be the equal. AB/AD= BC/CD Now we shall prove it using similar triangles. Unfortunate to us these two triangles are not necessarily equal to each other. We don’t know whether angle A is equal to angle C etc. Thus to proof ourselves we need to use the mathematicstheorem by using the ratios.

We will have to construct the set of triangles these types .If we continue the angle bisector line keep going from D and draw a line parallel to AB and create a line from C and name it as F. Thus, FC parallel to AB. This way we can look like two triangles look similar. The two triangles are ADB and CDF.As understood that AB and FC are parallel and BD is transversal and we also know that angle ABD is equal to angle CBD and because BD is a bisector angle the using transversal angles as we studies the DBC is equal to angle CFD.

When we look at the largest triangle BFC, There bases are same it is called as Isosceles triangle. So BC must be the same as FC. we have not proved yet, thus when we take a look on triangle ABD and CFD, the angle ADB is equal to angle FDC cause the vertical angles are equal. Thus we know that in a triangle when two angles are similar the third one also become same. Triangle BDA is similar to Triangle FDC. By the corresponding sides to be equal, we have AB/AD = CF/CD as CF is equal to BC as we proved it. Thus angle bisector of an angle in a triangle which separates the opposite side in the same ratio as the sides adjacent to the angle.

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