Hello friends. In this blog we will learn about the isosceles triangles and the theorems related to such triangles. The isosceles triangles are used in the geometry of grade IX standard of the geometry mathematics. As per the definition of the isosceles triangles, the isosceles triangles are those triangles whose two sides are congruent to each other; this means that a triangle which has its two sides equal is an isosceles triangle. Now if the two opposite sides of any triangles are equal then the both opposite angles will also be equal in the magnitude. The figure of the isosceles triangles can be given as:
Now, let us talk about the isosceles triangle theorems. The theorem for isosceles triangles states that the angles apposite the both equal sides are also equal. The isosceles triangle theorems with their relative proof can now be given as:
Theorem: The first theorem for isosceles triangle states that if the two sides of a triangle are congruent (Congruent stands for similarity in the shape and size of the sides in triangle) then the angles opposite them will also be congruent. To prove the theorem, let us draw a triangle XYZ in which two of the sides (side XY and side YZ) of triangle are congruent to each other. For the purpose of proving let us draw a bisector line YM, which intersects the base line XZ at a mid point M. Now the two triangles XYM and ZYM in the original triangle XYZ are congruent to each other. They are congruent because the line YM is common between them and also congruent sides for both triangles and that’s why the other lines XY and YZ both are also congruent. The angles between them (angle XYM and angle ZYM) are also congruent to each other and from figure angle YXZ and YZX are both corresponding angles of the triangles XYM and ZYM. So, they are also congruent. Hence it is proved that the angles opposite the both equal sides are also equal. (To get help on ICSE Board Syllabus click here)
The same theorem in some other words can also be explained as, that if two opposite angles of a triangle are equal then the opposite sides will also be congruent and In the next session we will discuss about time and angle measures.
Now, let us talk about the isosceles triangle theorems. The theorem for isosceles triangles states that the angles apposite the both equal sides are also equal. The isosceles triangle theorems with their relative proof can now be given as:
Theorem: The first theorem for isosceles triangle states that if the two sides of a triangle are congruent (Congruent stands for similarity in the shape and size of the sides in triangle) then the angles opposite them will also be congruent. To prove the theorem, let us draw a triangle XYZ in which two of the sides (side XY and side YZ) of triangle are congruent to each other. For the purpose of proving let us draw a bisector line YM, which intersects the base line XZ at a mid point M. Now the two triangles XYM and ZYM in the original triangle XYZ are congruent to each other. They are congruent because the line YM is common between them and also congruent sides for both triangles and that’s why the other lines XY and YZ both are also congruent. The angles between them (angle XYM and angle ZYM) are also congruent to each other and from figure angle YXZ and YZX are both corresponding angles of the triangles XYM and ZYM. So, they are also congruent. Hence it is proved that the angles opposite the both equal sides are also equal. (To get help on ICSE Board Syllabus click here)
The same theorem in some other words can also be explained as, that if two opposite angles of a triangle are equal then the opposite sides will also be congruent and In the next session we will discuss about time and angle measures.
No comments:
Post a Comment