# Straight Line Drawn from the Vertex of a Triangle to the Base

Here we will prove that any straight line drawn from the vertex of a triangle to the base is bisected by the straight line which joins the middle points of the other two sides of the triangle.

Solution:

Given: Q and R are the midpoints of the sides XY and XZ respectively of ∆PQR. P is any point on the base YZ. QR cuts XP at M.

To prove:  QR bisects XP, i.e., XM = MP.

Proof:

 Statement Reason 1. QR ∥YZ. 1. By the Midpoint Theorem. 2. In ∆XYP, Q is the midpoint of XY and QM ∥ YP. 2. From statement 1. 3. QM bisects XP. 3. By the converse of Midpoint Theorem. 4. XM = MP. (Proved) 4. From statement 3.

From Straight Line Drawn from the Vertex of a Triangle to the Base to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles 1. ### Cardinal Numbers and Ordinal Numbers | Cardinal Numbers | Ordinal Num

Dec 07, 23 01:27 AM

Cardinal numbers and ordinal numbers are explained here with the help of colorful pictures. There are many steps in a staircase as shown in the above figure. The given staircase has nine steps,

2. ### Smallest and Greatest Number upto 10 | Greater than | Less than | Math

Dec 06, 23 11:21 PM

We will discuss about the smallest and greatest number upto 10.