1. Midsegments of Triangles
Unit 7 Lesson 15-1
Midsegments of Triangles

2. Warm-Up
Pick up “Exploring Midsegments of a Triangle” half sheet on the back table.
Grab a protractor from the back cart for a straight edge.
Grab a calculator.
Complete #1 and #2 on the “Exploring Midsegments of a Triangle” half sheet.

3. Pythagorean Theorem or Distance Formula!!
a2 + b2 = c2
= c2
= c2
100 = c2
10 = c
a2 + b2 = c2
= c2
= c2
169 = c2
13 = c T R K 6 6 10 c 8
14.318 c
a2 + b2 = c2
= c2
= c2
205 = c2
= c 13 c 5 13 12 10 13
14.318
Pythagorean Theorem or Distance Formula!!

4. TU
a2 + b2 = c2
= c2
= c2
25 = c2
5 = c UR
a2 + b2 = c2
= c2
= c2
25 = c2
5 = c UY
a2 + b2 = c2
= c2
= c2
51.25 = c2
7.159 = c T R K 5 U TY
a2 + b2 = c2
= c2
= c2
42.25 = c2
6.5 = c YK
a2 + b2 = c2
= c2
= c2
42.25 = c2
6.5 = c 5
14.318
7.159
6.5 Y
6.5 5 5
6.5
6.5
7.159

5. Two sides of the triangle are being bisected.
One side of the triangle is half the length of another side.
The slopes of the midsegment and the 3rd side are the same,
therefore they are parallel.
A midsegment of a triangle is a segment that connects two
midpoints of a triangle. It bisects two sides of the triangle and
is half the length of the third side.

6. Practice #1 18 y 2 x z 6 2 9
x = _____
y = _____
z = _____

7. 5 7 Practice #2 x = _____ y = _____ x + 18 = 7x – 12 18 = 6x – 12
2(2y + 25) = 11y + 1
4y + 50 = 11y + 1
50 = 7y +1
49 = 7y
y = 7 5 7
x = _____
y = _____

8. Application x = 86 ft. 52 ft sink hole X 52 ft 43 ft 30 ft 30 ft
How could you use midsegments to determine the maximum width
of an oil spill?
Find the maximum width of the oil spill with the given distances.
x = 86 ft.

9. Midsegments in trapezoids
average

10. Practice #1 12
= 46
46/2 = 23 23 34

11. Practice #2 3x - 4 (3x – 4 + 28)/2 = 3x 3x – 4 + 28 = 6x -4 + 28 = 3x

12. Sides of small triangle
Multiple midsegments
Properties of multiple midsegments: 4
congruent
Triangles formed
Sides of small triangle
are ½ of the
original
1 small
triangle is
similar to a large
Area of
small triangle
is ¼ the original