Triangles are the polygons with three sides. We say that the triangle is the closed figure with three sides. Now we need to know that the Triangles are classified as per the measure of their lengths of their sides. We say that the triangles which have all the sides of the same measure, then the triangles are called equilateral triangles.
Now we will talk about isosceles triangles: An Isosceles Triangle has two equal sides and the third side is unequal, which works as the base of the triangle. If we look at the special properties of the isosceles triangle, we say:
As isosceles triangle have two lines of same length
As the two sides of the triangle are same, we say that the angles corresponding to the equal sides are also equal.
Also the Median of the isosceles triangle, drawn from non equal side, is also the perpendicular bisector of the non equal side.
As we know that the sum of the three angles of the triangle are equal, thus if one angle of the triangle is known, we are able to find the remaining two angles of the isosceles triangle. Let us see how: If the triangle has one angle = 70 degree, then if we want to find the measure of two angles of the triangle, which are unequal. Let the measure of those angles = x degrees. Now we say that 70 + x + x = 180,
2x + 70 = 180,
2x = 180- 70,
2x = 110,
X = 55, so other two angles of the triangle are 55 and 55 degrees
Similarly, if we know the two equal angles of the triangle, then we double the measure and then subtract it from 180 degrees to get the third angle of the triangle.
Points Shown above are the Special Features of Isosceles Triangles.
Special Features of Isoceles Triangles.
An Isosceles Triangle With A Specifies Vertex Angle
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Triangles are classified according to their length of the line segments and as per their angles. We know that if we have the Triangles classified as per the length of their line segments then the triangles are of following types: 1. Equilateral Triangle 2. Isosceles triangle 3. Scalene triangle. Here we are going to study about an Isosceles Triangle. Triangles with the same length of their two sides are called isosceles triangles. As the lengths of the two sides of the isosceles triangles are same, so the sides corresponding to the equal sides of the isosceles triangle are also equal. Now we observe that An Isosceles triangle with a specifies Vertex angle is known then we say that we have the measure of one of the angle of the triangle and the other two sides are equal, then we can find the measure of the angles which are of the same measure. We say that the triangle has the angle sum measure of 180 degrees, which means that the sums of all the three angles of the triangle are equal. Now if we have the vertex angle of 50 degree. Let us assume that the measure of the angles of the same side be ‘x’. Thus we come to the conclusion that the sum of the three angles of the triangles in 180 degrees. So we can write it mathematically as follows:
50 + x + x = 180 degrees. It can also be written as follows:
50 + 2x = 180 degrees,
Or 2x = 180 – 50 degrees,
Or, we get 2x = 130 degrees,
Or, we get x = 130 / 2 = 65 degree each,
Thus we conclude that the measure of the three angles of the isosceles triangle will be 50, 65 and 65 degrees.
A Median of a triangle is defined as the line segment which is used to join a vertex of a triangle to the midpoint of the opposite sides of a triangle. There are three vertices present in a triangle, so three medians are present in a triangle. Median value depends on the vertices. There are some properties of An Isosceles Triangle with a median which are:
All the three medians of a triangle meet at a single Point or vertex to the opposite side of a triangle.
Every median which are present in a triangle divides the triangle into two similar Triangles and both triangle have same area.
Three median of a triangle divides the triangle into six equal parts of smaller triangles and the area of all the triangles is same and the shapes of all the triangles are different but the area is same.
Every median of a triangle is also an Altitude and a bisector of a triangle.
And every bisector of a triangle is also an altitude and a median of a triangle.
Now we see the median of an isosceles triangle.
The median of an isosceles triangle is half of the hypotenuse. An isosceles triangle one angle is Right Angle.
We can say that the median cut the triangle into two half and the two triangle ‘stw’ and ‘suw’ are equal. Both the triangles are congruent. One side of a triangle is right angle and when median is passing through the midpoint of a triangle. Now the angles are of 45 degree. We see in the diagram the Line Segment ‘st’ is equal to ‘su’. Since, we can say that the triangle ‘stu’ is an isosceles triangle.
Here in this diagram ‘sw’ is the median of a Line Segment ‘tu’. So the line segment ‘tw’ is equal to ‘uw’.