This article provides you with the concept of a Straight line drawn from the vertex of a triangle to the base. Children are aware of the topics triangles and straight lines. Here, we will learn and prove how a triangle bisects the opposite side by a straight line with the help of the midpoint theorem. A triangle is a polygon shape formed by three line segments with three midpoints respectively.
By the end of this page, kids will perceive how a line bisects the other side. Without any delay let us discuss the concept and prove the statement. On this page, we have also given a glimpse on the topics called median and the centroid of a triangle for a better understanding of the Straight Line Drawn from the Vertex of a Triangle to the Base.
Also, Refer:
Median
A median is defined as the line segment joining a vertex of the opposite side of a triangle and bisects the side. In other words, a straight line drawn from one vertex to the opposite of the vertex of a triangle is called a median and every triangle has three medians. Learn the concept of the median of raw data and gain proper knowledge on how to solve it easily.
The Centroid of a Triangle
A triangle is formed by joining three dots by a line segment connected to each other and forms a triangle. A triangle has three medians with three angles. A centroid is defined as “the point of intersection of three medians of a triangle”.
For example, if we take a triangle ABC we have three midpoints D, E, and F respectively. Here, O is the point of intersection of three medians and O is a centroid of a triangle. The below figure gives how a centroid of a triangle looks like.
Properties of a Centroid
The properties of a centroid are as follows
- It is a point of congruency.
- Centroid is the intersection of three medians and bisects on the opposite side.
- A centroid is always inside of a triangle.
- It divides each median in the ratio of 2:1.
Statement
A straight line drawn from the vertex of a triangle to the base is bisected by the straight line which joins the midpoints of the other two sides of the triangle.
To Prove:
Consider a triangle PQR.
Given M, N, and O are the midpoints of PQ, PR, and QR respectively.
We have to prove that MN bisects PO i.e., PX = XO.
Construction:
From the above △PQR, join the midpoints M, N, and O of a triangle and name the intersection point of a triangle as X.
The above figure is the constructed triangle PQR, to prove the theorem statement.
Proof of the Theorem:
Given PQR is a triangle.
Let M be the midpoint of PQ, N be the midpoint of PR, and O be the midpoint of QR.
O is the midpoint of QR then PO is the straight line that bisects MN at point O.
Since M and N are the midpoints of the sides PQ and PR of a △PQR, then
MN ∥ QR by the midpoint theorem.
since MN ∥ QR, then MX ∥ QO.
In △PQO, we know that M is the midpoint of PQ and X be the midpoint of PO.
By converse of midpoint theorem
MX ∥ QO
⇒ PX=XO.
Thus, MN bisects PO.
Hence, the statement Straight Line Drawn from the Vertex of a Triangle to the Base is proved.
FAQ’s on Prove that a Line Drawn from the Vertex to its Base is a Straight Line
1. What do you call the straight line joining the vertex with the center of the base?
In mathematics, a triangle is a line segment that joins the vertex to the midpoint of the opposite side, it bisects the side. Every triangle has three medians from each vertex and all three midpoints intersect each other and it is known as the centroid of a triangle.
2. What is called the line joining vertex and the midpoint of the base of the triangle?
The line segment joining a vertex of a triangle to the midpoint of a triangle is known as the median. Every triangle has three medians and three altitudes.
3. What is the base of a triangle?
The base of a triangle is the bottom line of a triangle, and it is one of the three sides of a triangle. But in a triangle, one side is a base side and the remaining two sides are the height and the hypotenuse side of a triangle.
4. What is the vertex of a triangle?
The vertex or vertices are the corners of a triangle. There will be three vertices for every triangle.