How do you prove the midpoint theorem?

How do you prove the midpoint theorem?

To verify the mid-point theorem for a triangle.

1. Theorem : The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
2. Given in the figure A : AP=PB, AQ=QC.
3. To prove: PQ || BC and PQ=1/2 BC.
4. Plan: To prove ▲ APQ ≅ ▲ QRC.

Which theorem will prove DE is parallel to BC and DE ½ BC?

The midpoint theorem
The midpoint theorem says that DE will be parallel to BC and equal to exactly half of BC. Look at the image given below to understand the triangle midpoint theorem.

What is mid point theorem Class 10?

The midpoint theorem states that ” The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

What is midpoint theorem and prove it?

MidPoint Theorem Proof If the line segment adjoins midpoints of any of the sides of a triangle, then the line segment is said to be parallel to all the remaining sides, and it measures about half of the remaining sides. DE = (1/2 * BC).

Can we prove midpoint theorem using BPT?

Also, the converse of mid-point theorem is also true which states that the line drawn through the mid-point of a side of a triangle which is parallel to another side, bisects the third side of the triangle. Hence, the basic proportionality theorem is proved.

What is converse midpoint theorem?

The converse of the midpoint theorem states that ” if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side”.

What is mid point theorem and its proof?

MidPoint Theorem Proof If the line segment adjoins midpoints of any of the sides of a triangle, then the line segment is said to be parallel to all the remaining sides, and it measures about half of the remaining sides. Let E and D be the midpoints of the sides AC and AB.

What is mid-point theorem and its proof?

What is BPT and converse of BPT?

Basic Proportionality Theorem – A line drawn parallel to one side of a triangle and cutting the other two sides, divides the other two sides in equal proportion. The converse of Basic Proportionality Theorem – A line drawn to cut two sides of a triangle in equal proportion is parallel to the third side.

What is the proof of mid point theorem?

MidPoint Theorem Proof . If midpoints of any of the sides of a triangle are adjoined by the line segment, then the line segment is said to be in parallel to all the remaining sides and also will measure about half of the remaining sides. Oct 22 2019

What is the definition of midpoint theorem?

In Coordinate Geometry, midpoint theorem refers to the midpoint of the line segment. It defines the coordinate points of the midpoint of the line segment can be found by taking the average of the coordinates of the given endpoints. The midpoint formula is used to determine the midpoint between the two given points. Oct 22 2019

What is the triangle midpoint theorum?

The midpoint theorem states that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side. Whereas, its converse states that the line drawn through the midpoint of one side of a triangle and parallel to another side bisects the third side.

How do you find the midpoint of a triangle?

To find the midpoint, measure the side, and divide the length in half. Label the midpoint A. For example, if one side of the triangle is 10 cm long, the midpoint will be at 5 cm, since 10/2=5{\\displaystyle 10/2=5}. 2. Find the midpoint of a second side of the triangle.