Holt Geometry 5-4 The Triangle Midsegment Theorem WARM-UP The vertex angle of an isosceles triangle...
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Holt Geometry 5-4 The Triangle Midsegment Theorem 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.
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Transcript of Holt Geometry 5-4 The Triangle Midsegment Theorem WARM-UP The vertex angle of an isosceles triangle...
Holt Geometry
5-4 The Triangle Midsegment TheoremWARM-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.
Holt Geometry
5-4 The Triangle Midsegment Theorem
The Triangle Midsegment Theorem
Holt Geometry
5-4 The Triangle Midsegment Theorem
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.
Holt Geometry
5-4 The Triangle Midsegment TheoremDeveloping the Triangle Midsegment Theorem
1. Cut out triangle ABC.
Holt Geometry
5-4 The Triangle Midsegment TheoremDeveloping 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.
Holt Geometry
5-4 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.
Developing the Triangle Midsegment Theorem
3. Fold the triangle on line LN.
Holt Geometry
5-4 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.
Developing the Triangle Midsegment Theorem
3. Fold the triangle on line LN.
4. Fold A to C.
Holt Geometry
5-4 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.
Developing the Triangle Midsegment Theorem
3. Fold the triangle on line LN.
4. Fold A to C.
5. Fold B to C.
Holt Geometry
5-4 The Triangle Midsegment Theorem
The Triangle Midsegment Theorem
Holt Geometry
5-4 The Triangle Midsegment Theorem
Is XY a midsegment of the triangle?
Holt Geometry
5-4 The Triangle Midsegment Theorem
Find:
1.
2.
€
m∠SVU€
UW
Holt Geometry
5-4 The Triangle Midsegment Theorem
Find:
1.
2.
3.
€
JL
€
PM
€
m∠MLK
Holt Geometry
5-4 The Triangle Midsegment Theorem
Would isosceles and equilateral triangles have congruent midsegments? Explain why or why not.
Holt Geometry
5-4 The Triangle Midsegment TheoremYou 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
INDIRECT MEASUREMENT
Holt Geometry
5-4 The Triangle Midsegment TheoremREAL WORLD APPLICATIONS
1.What is the distance across the volcano?
2. What is the length of the bridge?
3. 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?
Holt Geometry
5-4 The Triangle Midsegment Theorem
Algebra and Midsegments
Holt Geometry
5-4 The Triangle Midsegment Theorem
Algebra and Midsegments
Holt Geometry
5-4 The Triangle Midsegment Theorem
EXIT TICKET
Holt Geometry
5-4 The Triangle Midsegment Theorem
Warm-Up
1. Find the value of n.
2. ∆XYZ is the midsegment triangle of ∆WUV.
What is the perimeter of ∆XYZ?
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