Math Problem Statement

Decide whether the statement about the diagram is true. Explain your answer using the definitions you have learned.

Solution

The problem asks whether the statement about the diagram is true based on the definition of perpendicular lines.

From the diagram, lines PQPQ and STST are shown intersecting at a right angle (90°), which is indicated by the symbol \perp (perpendicular).

Definitions:

  1. Perpendicular lines: Two lines are perpendicular if they intersect to form a right angle (90°).

Based on this, the correct answer should be:

  • True; if intersecting lines form a right angle, then they are perpendicular.

Explanation: The definition of perpendicular lines is that they meet at a right angle (90°). In the diagram, this is the case for PQSTPQ \perp ST, so the statement is true.

Do you want more details or have any questions?

Here are some related questions you might want to explore:

  1. How can we verify if two lines are perpendicular without measuring angles?
  2. Can lines in 3D space also be perpendicular?
  3. What happens when two lines intersect but do not form a right angle?
  4. What is the relationship between perpendicular and parallel lines?
  5. Can two perpendicular lines share more than one point of intersection?

Tip: In geometry, the perpendicular symbol (\perp) always indicates that two lines intersect at a right angle (90°).

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Math Problem Analysis

Mathematical Concepts

Geometry
Perpendicular Lines
Angles

Formulas

-

Theorems

Perpendicularity Theorem

Suitable Grade Level

Grade 6-8