1. WARM-UP
The vertex angle of an isosceles triangle measures
(a + 15)°, and one of the base angles measures 7a°.
Find a and each angle measure.

2. The Triangle Midsegment Theorem

3. A midsegment of a triangle is a segment that joins the midpoints of two sides of the triangle. Every triangle has three midsegments, which form the midsegment triangle.

4. Developing the Triangle Midsegment Theorem
1. Cut out triangle ABC.

5. Developing the Triangle Midsegment Theoremc
1. Cut out triangle ABC.
2. Fold A onto C to find the midpoint
of AC. Mark this point as L. Fold B
onto C to find the midpoint of BC.
Mark this point as N. Draw a line
from L to N.

6. Developing the Triangle Midsegment Theorem
1. Cut out triangle ABC.
2. Fold A onto C to find the midpoint
of AC. Mark this point as L. Fold B
onto C to find the midpoint of BC.
Mark this point as N. Draw a line
from L to N.
3. Fold the triangle on line LN.

7. Developing the Triangle Midsegment Theorem
1. Cut out triangle ABC.
2. Fold A onto C to find the midpoint
of AC. Mark this point as L. Fold B
onto C to find the midpoint of BC.
Mark this point as N. Draw a line
from L to N.
3. Fold the triangle on line LN.
4. Fold A to C.

8. Developing the Triangle Midsegment Theorem
1. Cut out triangle ABC.
2. Fold A onto C to find the midpoint
of AC. Mark this point as L. Fold B
onto C to find the midpoint of BC.
Mark this point as N. Draw a line
from L to N.
3. Fold the triangle on line LN.
4. Fold A to C.
5. Fold B to C.

9. The Triangle Midsegment Theorem

10. Is XY a midsegment of the triangle?

11. Find: 1. 2.

12. Find: 1. 2. 3.

13. Would isosceles and equilateral triangles have
congruent midsegments? Explain why or why
not.

14. INDIRECT MEASUREMENT
You are a geologist whose job is to measure the distance
across a sinkhole. You cannot measure directly across
the sinkhole, so you must find some other way to
find the distance across, using only measures you can
take on the ground.
Use the diagram and a ruler to find the distance from A to
B across the sinkhole.
On the diagram,
1 inch = 40 feet

15. REAL WORLD APPLICATIONS
What is the distance
across the volcano?
2. What is the length of the bridge?
A new street is planned in the town of Springfield.
Parallel parking will be available all along the new
street, on both sides. If each parking space is 23 feet
long, about how many parking spaces will the new
street accommodate?

16. Algebra and Midsegments

17. Algebra and Midsegments

18. EXIT TICKET

19. Warm-Up
1. Find the value of n.
2. ∆XYZ is the midsegment triangle of ∆WUV. What is the perimeter of ∆XYZ? 16
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