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Questions and Answers
What is the definition of congruence?
What is the definition of congruence?
- A property that only applies to angles.
- Segments that have different measures.
- Segments that have the same measure. (correct)
- A measure of angle relationships.
What does the midpoint of a segment do?
What does the midpoint of a segment do?
It divides the segment into 2 equal parts.
What does the Segment Addition Postulate state?
What does the Segment Addition Postulate state?
If A, B, and C are collinear points and B is between A and C, then AB + BC = AC.
The Reflexive Property of Congruence states that for any segment AB, AB ≅ BC.
The Reflexive Property of Congruence states that for any segment AB, AB ≅ BC.
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According to the Symmetric Property of Congruence, if AB ≅ CD, then CD ≅ AB.
According to the Symmetric Property of Congruence, if AB ≅ CD, then CD ≅ AB.
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The Transitive Property of Congruence asserts that if AB ≅ CD and CD ≅ EF, then AB ≅ EF.
The Transitive Property of Congruence asserts that if AB ≅ CD and CD ≅ EF, then AB ≅ EF.
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Study Notes
Definitions of Key Terms
- Congruence: Segments AB and CD are congruent if they have equal measures, represented as AB ≅ CD implies AB = CD.
- Midpoint: The midpoint (M) of a segment divides it into two equal parts, ensuring AM = MB for segment AB.
Fundamental Principles
- Segment Addition Postulate: For collinear points A, B, and C, if B lies between A and C, then the sum of segments AB and BC equals segment AC (AB + BC = AC).
- Reflexive Property of Congruence: A segment is always congruent to itself; thus, for any segment AB, it holds that AB ≅ AB.
- Symmetric Property of Congruence: If segment AB is congruent to segment CD, then segment CD is also congruent to segment AB (if AB ≅ CD, then CD ≅ AB).
- Transitive Property of Congruence: If segment AB is congruent to segment CD and segment CD is congruent to segment EF, then segment AB is congruent to segment EF (if AB ≅ CD and CD ≅ EF, then AB ≅ EF).
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