Proving the Midsegment of a Triangle Adapted from Walch
Education
Slide 3
Key Concepts In the diagram, the midpoint of is X. The midpoint
of is Y. A midsegment of is. 21.9.3: Proving the Midsegment of a
Triangle The midpoint is the point on a line segment that divides
the segment into two equal parts. A midsegment of a triangle is a
line segment that joins the midpoints of two sides of a
triangle.
Slide 4
Key Concepts, continued The midsegment of a triangle is
parallel to the third side of the triangle and is half as long as
the third side. This is known as the Triangle Midsegment Theorem.
Every triangle has three midsegments. 31.9.3: Proving the
Midsegment of a Triangle
Slide 5
4 Theorem Triangle Midsegment Theorem A midsegment of a
triangle is parallel to the third side and is half as long.
Slide 6
Key Concepts, continued When all three of the midsegments of a
triangle are connected, a midsegment triangle is created. 51.9.3:
Proving the Midsegment of a Triangle
Slide 7
Key Concepts, continued Coordinate proofs, proofs that involve
calculations and make reference to the coordinate plane, are often
used to prove many theorems. 61.9.3: Proving the Midsegment of a
Triangle
Slide 8
Practice The midpoints of a triangle are X (2, 5), Y (3, 1),
and Z (4, 8). Find the coordinates of the vertices of the triangle.
71.9.3: Proving the Midsegment of a Triangle
Slide 9
Plot the midpoints on a coordinate plane. 81.9.3: Proving the
Midsegment of a Triangle
Slide 10
Connect the midpoints to form the midsegments 91.9.3: Proving
the Midsegment of a Triangle
Slide 11
Calculate the slope of each midsegment Calculate the slope of.
The slope of is. 101.9.3: Proving the Midsegment of a Triangle
Slope formula Substitute (2, 5) and (3, 1) for (x 1, y 1 ) and (x
2, y 2 ). Simplify.
Slide 12
Calculate the slope of each midsegment Calculate the slope of.
The slope of is 7. 111.9.3: Proving the Midsegment of a Triangle
Slope formula Substitute (3, 1) and (4, 8) for (x 1, y 1 ) and (x
2, y 2 ). Simplify.
Slide 13
Calculate the slope of each midsegment Calculate the slope of.
The slope of is. 121.9.3: Proving the Midsegment of a Triangle
Slope formula Substitute (2, 5) and (4, 8) for (x 1, y 1 ) and (x
2, y 2 ). Simplify.
Slide 14
Draw the lines that contain the midpoints. The endpoints of
each midsegment are the midpoints of the larger triangle. Each
midsegment is also parallel to the opposite side. 131.9.3: Proving
the Midsegment of a Triangle
Slide 15
Draw the lines that contain the midpoints. The slope of is.
From point Y, draw a line that has a slope of. 141.9.3: Proving the
Midsegment of a Triangle
Slide 16
Draw the lines that contain the midpoints. The slope of is 7.
From point X, draw a line that has a slope of 7. 151.9.3: Proving
the Midsegment of a Triangle
Slide 17
Draw the lines that contain the midpoints. The slope of is.
From point Z, draw a line that has a slope of. The intersections of
the lines form the vertices of the triangle. 161.9.3: Proving the
Midsegment of a Triangle
Slide 18
Determine the vertices of the triangle. The vertices of the
triangle are (3, 2), (9, 4), and (1, 12), as shown on the following
slide. 171.9.3: Proving the Midsegment of a Triangle