Discover that the line joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.
The line segment joining the midpoints of two sides of a triangle is parallel to the third side and equal to half its length.
In triangle ABC, D and E are midpoints of AB and AC. If BC=12 cm, find DE.
DE=½×BC=6 cm, and DE is parallel to BC
If DE (joining midpoints) = 8 cm, find the length of the third side.
Third side=2×DE=16 cm
The converse states: if a line through the midpoint of one side is parallel to another side, it bisects the third side. This connects to the intercept theorem for parallel lines.
A line through the midpoint of AB in triangle ABC is drawn parallel to BC. What can we conclude?
By the converse of the mid-point theorem, this line bisects AC too
Three parallel lines cut two transversals into equal parts on one transversal. What can be said about the other transversal?
By the intercept theorem, the parts on the other transversal are also equal
1. In triangle PQR, M and N are midpoints of PQ and PR. If QR=18 cm, find MN.
2. If MN (joining midpoints)=5 cm, find the length of the corresponding third side.
3. A line through the midpoint of one side of a triangle, parallel to a second side, does what to the third side?
4. In a triangle with sides 10 cm, 14 cm, 16 cm, find the perimeter of the triangle formed by joining the midpoints.
5. What is the relationship between the triangle formed by joining all three midpoints and the original triangle?