Problem Analysis:
The image presents a quantitative comparison problem involving a triangle. The task is to compare
Quantity A and
Quantity B based on the given information.
#### Given Information:
1. The triangle is labeled with vertices \( X \), \( Y \), and \( Z \).
2. The sides of the triangle are labeled as follows:
- \( XY = a \)
- \( YZ = b \)
- \( XZ = c \)
3. The condition \( XY = YZ = XZ \) is highlighted, indicating that all three sides of the triangle are equal.
4.
Quantity A is labeled as \( a \).
5.
Quantity B is labeled as \( c \).
#### Key Observations:
- The condition \( XY = YZ = XZ \) implies that the triangle is an
equilateral triangle. In an equilateral triangle, all three sides are of equal length.
- Therefore, \( a = b = c \).
Step-by-Step Solution:
1.
Identify the nature of the triangle:
- Since \( XY = YZ = XZ \), the triangle is equilateral.
- In an equilateral triangle, all sides are equal in length.
2.
Relate the quantities:
- \( a \) represents the length of side \( XY \).
- \( c \) represents the length of side \( XZ \).
- Since the triangle is equilateral, \( a = c \).
3.
Compare Quantity A and Quantity B:
- Quantity A is \( a \).
- Quantity B is \( c \).
- From the equilateral property, \( a = c \).
Conclusion:
Since \( a = c \), the two quantities are equal.
Final Answer:
\[
\boxed{\text{The two quantities are equal.}}
\]
Parent Tip: Review the logic above to help your child master the concept of quantitative comparison worksheet.
