Question content area top
Part 1
The distinct lines​ a, b,​ c, and d are in the same plane. Tell how a and d relate. Justify your answer.
a
font size decreased by 5 | font size decreased by 5 | font size decreased by 5
b comma
b
font size decreased by 5 Start 1 By 2 Table 1st Row 1st Column 2nd Column EndTable
 
c comma
c
font size decreased by 5 | font size decreased by 5 | font size decreased by 5
d
Question content area bottom
Part 1
Choose the correct answer below.
A.
a is perpendicular to d because a is perpendicular to c and c is parallel to d.
B.
a is parallel to d because a is parallel to c and c is parallel to d.
C.
a is parallel to d because a is perpendicular to c and c is parallel to d.
D.
a is perpendicular to d because a is parallel to c and c is parallel to d.

To solve this, let's break down the problem:

- We are given four distinct lines \( a \), \( b \), \( c \), and \( d \) that are all in the same plane.
- We need to determine how line \( a \) relates to line \( d \), based on the relationships between the other lines.

Now, let's analyze each option:

### Option A: 
- "Line \( a \) is **perpendicular** to line \( d \) because line \( a \) is **perpendicular** to line \( c \) and line \( c \) is **parallel** to line \( d \)."
  
  - If \( a \perp c \) and \( c \parallel d \), then \( a \) must also be **perpendicular** to \( d \), because perpendicular lines to one parallel line will be perpendicular to the other.

  **This seems correct**, but let's check the other options.

### Option B: 
- "Line \( a \) is **parallel** to line \( d \) because line \( a \) is **parallel** to line \( c \) and line \( c \) is **parallel** to line \( d \)."
  
  - If both \( a \parallel c \) and \( c \parallel d \), then by transitivity, \( a \parallel d \).

  **This also seems possible**.

### Option C: 
- "Line \( a \) is **parallel** to line \( d \) because line \( a \) is **perpendicular** to line \( c \) and line \( c \) is **parallel** to line \( d \)."
  
  - If \( a \perp c \) and \( c \parallel d \), this would make \( a \perp d \), **not parallel** to \( d \). So, this option is **incorrect**.

### Option D: 
- "Line \( a \) is **perpendicular** to line \( d \) because line \( a \) is **parallel** to line \( c \) and line \( c \) is **parallel** to line \( d \)."
  
  - If both \( a \parallel c \) and \( c \parallel d \), then \( a \parallel d \), **not perpendicular**. This is **incorrect**.

### Conclusion:
- The correct answer is **B**: "Line \( a \) is **parallel** to line \( d** because line \( a \) is **parallel** to line \( c \) and line \( c \) is **parallel** to line \( d**.

Would you like further explanation? Here are 5 related questions:

1. What are the conditions for two lines to be parallel in the same plane?
2. How do transitive relationships between parallel lines work?
3. What happens if two lines are perpendicular to the same third line?
4. How would you describe the relationship between perpendicular and parallel lines in terms of angles?
5. What is the difference between parallel lines and skew lines?

**Tip:** Always visualize line relationships on a coordinate plane to better understand parallel and perpendicular conditions.

The distinct lines a, b, c, and d are in the same plane. Tell how a and d relate. Justify your answer. Part 1: Choose the correct answer below. A) a is perpendicular to d because a is perpendicular to c and c is parallel to d. B) a is parallel to d because a is parallel to c and c is parallel to d. C) a is parallel to d because a is perpendicular to c and c is parallel to d. D) a is perpendicular to d because a is parallel to c and c is parallel to d.

Discover the relationship between lines a and d, given that they are distinct lines in the same plane. This problem involves parallel and perpendicular line relationships, and uses key geometric theorems like the Transitive Property of Parallel Lines and Perpendicular Line Theorem. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation