Math Problem Statement
Solution
Let's solve the problem in the image.
Given Information:
- is a triangle with as midpoints of sides and respectively.
- (implies is the midpoint of ).
- (implies is the midpoint of ).
- , , and .
Required:
Find the length of .
Key Concept: Midsegment Theorem
The midsegment theorem states that:
- A midsegment of a triangle (a segment connecting the midpoints of two sides) is parallel to the third side.
- The length of the midsegment is half the length of the side it is parallel to.
Application:
- Since is the midsegment connecting (midpoint of ) and (midpoint of ), it is parallel to side .
- By the midsegment theorem, the length of is:
Substitution:
From the given information, . Thus:
Final Answer:
Let me know if you'd like further clarification!
Related Questions:
- What are the other midsegments of , and how can their lengths be calculated?
- How does the midsegment theorem help in proving similarity between triangles?
- What happens to the triangle if all three midsegments are drawn? What new figure is formed?
- Can the midsegment theorem be applied to a right triangle? If yes, how?
- How can the perimeter of the smaller triangle formed by midsegments be calculated?
Tip:
When working with midsegments, always identify the side they are parallel to—it simplifies the problem significantly!
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Math Problem Analysis
Mathematical Concepts
Geometry
Midsegments of a Triangle
Proportionality
Formulas
Midsegment = 1/2 * Length of Parallel Side
Theorems
Midsegment Theorem
Suitable Grade Level
Grades 8-10
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