Transcript Document

Triangle Midsegment Theorem
Lesson 55 Saxon Geometry
Warm-up Problems: Puzzle Packet
Puzzle Packet
Essential Questions
1. What is a midsegment of a triangle?
2. Which of the side lengths of a triangle
is the midsegment’s length half of?
3. Which of the side lengths of a triangle
is the midsegment parallel to?
4. How is a midsegment triangle related
to the original triangle?
New Concepts: Lesson 55
• A midsegment of a triangle is a segment that joins
the midpoints of two sides of the triangle. Every
triangle has three midsegments. The midsegment is
always half the length of the side that does not have
a midsegment endpoint on it.
Triangle Midsegment Theorem
Using the Triangle Midsegment Theorem
• In the diagram, DE is a midsegment
of  ABC. Find the values of x and y.
Your Turn: Using Triangle Midsegment Thm
• In the diagram, PQ is a midsegment
of  LMN. Find the values of x and y.
Theorem 55-2
Using Theorem 55-2
• In the diagram, what are the values of
a and b?
Identifying Midpoints of Sides of Triangles
• Triangle MNP has
vertices M(-2, 4), N(6, 2),
and P(2, -1). QR is a
midsegment of  MNP.
Find the coordinates of
Q and R.
Identifying Midpoints of Sides of Triangles
• Triangle ABC has
vertices A(-2, 1), B(4, 3),
and C(2,-2). DE is a
midsegment of  ABC
parallel to AC . Find the
coordinates of D and E.
Applying Similarity to Midsegment Problems
• Triangle STU is the midsegment triangle of
 PQR.
• a. Show that STU ∼ PQR.
• b. Find PQ.
Your Turn! Applying Similarity
• Triangle NOP is the midsegment triangle
of  KLM.
• a. Show that KLM ∼ NOP.
• b. Find the length of LK.
Video Summarizer
Written Practice
• L55 Practice p. 364 a, b, c, d
• Please; work with a partner.
Exit Slip
• p. 366 #15 & #30
• Individual Assessment