Math Problem Statement

Given: ΔABC Prove: A midsegment of ΔABC is parallel to a side of ΔABC.

Statement Reason

  1. Define the vertices of ΔABC to have unique points A(x1, y1), B(x2, y2), and C(x3, y3). given

  2. Let D be the midpoint of and E be the midpoint of . defining midpoints

  4. slope of

    slope of

definition of slope 5. slope of = slope of Transitive Property of Equality 6. is parallel to definition of parallel lines 7. Let F be the midpoint of . defining a midpoint 8. definition of midpoint 9. slope of

slope of

definition of slope 10. slope of = slope of Transitive Property of Equality 11. is parallel to . definition of parallel lines 12. Similarly, is parallel to . steps similar to steps 1-11 3 What is the reason for statement 3 in this proof? A. using point-slope formula B. definition of parallel lines C. Transitive Property of Equality D. Reflexive Property of Equality E. definition of midpoint Reset Next © 2024 Edmentum. All rights reserved.

Solution

The correct reason for statement 3 in this proof is:

E. definition of midpoint

In this context, the statement in question likely involves using the midpoint formula to find the coordinates of the midpoints D and E. The midpoint formula is used to calculate the point halfway between two points, and that aligns with the idea of defining the midpoints of the sides of the triangle.

Would you like a more detailed breakdown of this proof, or do you have any other questions?

Here are five related questions to expand on the topic:

  1. What is the midpoint formula, and how is it applied in geometry proofs?
  2. How can we use the slope formula to prove lines are parallel?
  3. Can the midsegment theorem be extended to non-right triangles?
  4. What are some real-life applications of midsegment and parallel lines?
  5. How do properties of triangles help in coordinate geometry?

Tip: Remember that the slope of parallel lines is always equal. This is key when proving lines are parallel using the slope formula.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Coordinate Geometry

Formulas

Midpoint Formula
Slope Formula

Theorems

Midsegment Theorem
Parallel Line Theorem

Suitable Grade Level

Grades 9-10

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