Page 133 - Math Course 3 (Book 2)

Proportional Parts of Triangles

MO. 10 - L4b
Let’s Begin

Dividing a Segment into Parts

Midsegment of a Triangle

Vocabulary A-Z Example

Let us learn some vocabulary
Triangle ABC has vertices A(–2, 2), B(2, 4) and
C(4, –4). DE is a midsegment of △ABC. Find the
midsegment coordinates of D and E.
The midsegment of a triangle (also called a
midline) is a segment joining the midpoints of y B
two sides of a triangle. D (2, 4)

A (–2, 2)
A

Midpoint D E Midpoint O x
Midsegment E

B C (4, –4)

C

THEOREM 10.6 Use the Midpoint Formula to find the midpoints of
AB and AC.

Triangle Midsegment Theorem –2 + 2 2 + 4
D , = D(0, 3)
A midsegment of a triangle is parallel to one side 2 2
of the triangle, and its length is one-half the length
of that side. –2 + 4 2 + (–4)
E , = E(1, –1)
2 2
Example: If B and D are midpoints of AC and EC,
1
respectively, BD || AE and BD = AE.
2 Answer D (0, 3), E (1, –1)
C

B D

A E

125