Each Geometry angles and each geometry side has its own name, which is called as a Special name for sides and angles. Now we discuss each and every Special name for sides and angles:
Angle BisectorBack to Top
To mark the angle bisector by protector, we need to first divide the angle by 2 and then mark that angle with the help of the protector and a pencil. Thus we find that the bisector of any angle exist at the midpoint of the given angle. It divides the given angle in two equal parts. We represent the bisector of any angle by a dotted line.
When we use the method of construction of drawing the angle bisector of any angle, we will first set a compass to a particular arc. Now place the compass at the vertex of the angle already drawn and mark the arc at the given angle. Now we observe that this arc cut the angle at two different points. We place the compass at these two different points and then mark the arc at the inner area of the angle which is already drawn. We observe that the arcs which we mark from two different points will intersect at a point. This Intersection point indicates the angle bisector of the given angle. We join it with the vertex of the given angle by a dotted line and we get the angle bisector of the given angle.
Base angleBack to Top
When two lines meet at same point is known as angle. Now we see the base angles theorem. The base angle theorem says that when two sides of a triangle are same then the angles which lie opposite to these sides are also equal or congruent.
If we talk about the Isosceles Triangle, the base angles of an isosceles triangle are also equal. Now we talk about converse of base angle i.e. when two angles of a triangle are same then opposite side’s angle are also same.
In figure of isosceles triangle it is shown that if two sides are congruent then the opposite sides of these angles are also congruent.
When we draw a perpendicular bisector from the point ‘z’ to the Line Segment ‘xy’, then it cuts the isosceles triangle into two equal parts, and after dividing both the Triangles are congruent then the Corresponding Angles are also equal.
The angle ‘z’ is bisected the triangle into two parts:
Here the triangle ‘xsz’ is equal to ‘ysz’.
And the line segments of both the triangles are also equal i.e.
The Line Segment ‘xz’ is equal to ‘yz’ and the line segments ‘zs’ are common in both the triangles. Both the triangles ‘xsz’ and triangle ‘ysz’ are congruent by SAS or side angle side. So we can say that the angle ‘x’ is equal to angle ‘y’. Now we see some of the attributes of a base angle which are.
Area – The number of space which are present inside a close figure.
Base – The side of a triangle from which we can assume the height of a triangle.
Base angle – The angle that is formed by the base and one side of an isosceles triangle, the base angle of an isosceles triangle are always equal. This shows the property of base angle.
Vertex angleBack to Top
The word vertex is used to denote the corners points of a Polygon. We can see the example of
Regular polygon – a polygon which has all sides and all interior angles are equal.
The vertex is a corner point of a polygon in which the number of sides and vertices are same or equal.
In case of triangle we can see a triangle has three vertices. We can say the number of vertices totally depend upon the number of sides.
We see the example of quadrilateral, a quadrilateral having many vertices because there are different types of quadrilateral such as square, rectangle, parallelogram, trapezoid, rhombus and kite. The vertices of a quadrilateral are dependent upon the number of sides.
The point of any figure from where we measure an angle vertex and any angle associated with the vertex is known as vertex angles.
In case of a polygon, the interior side of a vertex is denoted by ‘ai’ or ‘Ai’ and the sum of interior angles is given by (n – 2)⊼ radian or we calculate this value we get:
2(n – 2)* 90 degree,
Or the interior angles is also given by 180(n – 2),
Where ‘n’ are the number vertices.
We can also say that when two line segments meet at a same point or same vertex then two lines forms an included angle.
Sometimes the word vertex is used to indicate the top point, we can say that the vertex of an Isosceles Triangle.
Geometry MedianBack to Top
Now we will discuss a term related with median geometry which is ‘centroid’; Centroid of a triangle can be defined as a point where all 3 medians of a triangle meet. So we can say that centroid is the point of Intersection of all 3 medians. Centroid is also the center of mass of the object which has uniform density with triangular shape. So object can balance on a line passing through centroid of triangle.
Every median of the triangle partitions the area of a triangle in half. Medians of triangle partition the triangle into 6 small Triangles having equal area.
The centroid of the triangle partitions every median in the Ratio of 2 : 1, where centroid is twice as nearer to the midpoint of side as it is nearer to opposing side of the triangle.
This can be elaborated as,
3 / 4 (perimeter of triangle) < addition of medians < 3/2 (perimeter of the triangle).
Now if we have a triangle with sides’ p, q, r and medians mp, mq, mr.
Therefore 3 / 4 (p2 + q2 + r2) = mp2 + mq2 + mr2.
Median also divides the side of segment of triangle or we can say the side of triangle into 2 equal parts.
This is all about Geometry Median, and centroid of triangle.
Base and AltitudeBack to Top
Suppose we want to find the area of a triangle, as we know that it is half of the base multiplied by height, where the height of a triangle is the Altitude or we can say the perpendicular distance from the base to the opposite side vertex.
The base of a triangle can be any one side, it is not fixed.
IIn case of Isosceles Triangle the base is generally taken as side which is not equal to other sides. In case of quadrilateral, if a pair of equal side is present then both sides are called base of quadrilateral. The altitude of a quadrilateral is perpendicular distance from the base to the other side of a quadrilateral.
In the given figure you can easily see the base and altitude of a quadrilateral.
If we talk about the two faces of a Solid is said to be a base. So we can say that a cylinder has one base and a pyramid has only one base.
It is clear from the diagram of cylinder.
Now we will see how to draw Base and Altitude;
For construction of base and altitude we have to follow some steps which are given below:
Step1: First we take two lines segment PQ and RS which defines the base length and altitude of a triangle.
Step2: Then we draw a Point ‘A’ which becomes one end of the base of a triangle.
Step3: Now place the compass on point ‘R’ and measure the length ‘RS’ of the base of a triangle.
Step4: with the help of compass draw an arc from point ‘A’.
Step5: Mark point ‘B’, and draw a line ‘AB’, this is the other end of triangle.
Step6: Now measure the base length with the help of compass and draw an arc on each side of a base line from point ‘A’ and ‘B’.
Step7: We get the perpendicular bisector of the base which divides the base into two equal parts.
Step8: Now measure the distance of Point ‘PQ’, this is the altitude of a triangle.
Step9: Then put the compass on the midpoint of the base line and draw an arc across the perpendicular.
Step10: Then draw two sides AC and BC.
Step11: At last we get base and altitude of triangle.
This is the required figure.