Shown below are statements about geometric properties of lines. Select all of the statements that are true.
A. A ray extends infinitely in two directions.
B. Perpendicular lines intersect at a 90° angle.
C. Skew lines lie in the same plane but never intersect.
D. A transversal line intersects two or more other lines.
Answer (2)
A ray extends infinitely in one direction.
Perpendicular lines intersect at a 90° angle.
Skew lines do not lie in the same plane and never intersect.
A transversal line intersects two or more other lines.
The true statements are B and D. B , D
Explanation
Analyze the statements Let's analyze each statement to determine which ones are true.
Statement A Statement A: A ray extends infinitely in two directions. This is false. A ray extends infinitely in one direction.
Statement B Statement B: Perpendicular lines intersect at a 90° angle. This is true by the definition of perpendicular lines.
Statement C Statement C: Skew lines lie in the same plane but never intersect. This is false. Skew lines do not lie in the same plane.
Statement D Statement D: A transversal line intersects two or more other lines. This is true by the definition of a transversal line.
Conclusion Therefore, the true statements are B and D.
Examples
Understanding the properties of lines, such as perpendicular and transversal lines, is crucial in architecture and construction. For example, when designing a building, architects need to ensure that walls are perpendicular to the ground to provide stability. Transversal lines are also important in road design, where roads intersect at various angles.
The true statements are B (Perpendicular lines intersect at a 90° angle) and D (A transversal line intersects two or more other lines). Statements A and C are false because a ray extends in one direction, and skew lines do not lie in the same plane. Therefore, options B and D are correct.
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