Name: ______________________________________
Date:________________
Unit 5 Geometry: Relationships in Triangles and Quadrilaterals (Red)
Section 5.1
Midsegment Theorem and Coordinate Proof
Page 258- 263
Essential Question: How do you determine the midsegment of a triangle using the midsegment theorem?
Vocabulary:

A segment that connects the midpoints of two sides of a triangle is called ________________ ____ _____
_______________.

_______________ ______________ states that a segment that connects two sides of a triangle is parallel to the
third side AND is half as long as that third side.
EXAMPLE 1: Use the Midsegment Theorem to find lengths
In the diagram to below, ST and TU
are midsegments for ∆ PQR. Find
Using the Midsegment Theorem solve:
PR = ______ • ST
= ______ • _____
PR and TU using the midsegment
theorem.
= ___________
TU =
1
2
• _______
= ______ • _______
= _____________
YOU TRY:
1.
2.
Name: ______________________________________
Date:________________
EXAMPLE 2: Use Midsegment Theorem
In the diagram at the right, SB ≅ SC,
RS ⃦ AC, and RS =
1
2
AC. Show that
R is the midpoint of BA.
Solve:
Because SB ≅ SC, S is the ______________of BC.
1
RS ⃦ AC and RS = 2 AC, RS is a ____________________
of ∆ ABC by definition. _____________________
________________, R is the ____________________ of BA.
EXAMPLE 3: Place a figure in a coordinate plane
Place a figure in a coordinate plane in order to find the side lengths. Assign the coordinates to each vertex.
Figure: an isosceles triangle
Solution:
To find the horizontal and vertical segments of a figure, place one vertex on the __________. Then place one
or more sides on an ________ .
You Try:
3. Using the diagram below, if T is the midpoint of AC, what do you know about ST?
4. A rectangle has vertices at ( 0, 0), ( j,0), and ( j, k). Find the coordinates of the fourth vertex.