Question

Reduced and enlarged photographs of an object are _____.

• A. congruent
• B. similar
• C. not similar
• D. none

Hint:

Remember:
• Congruent = same shape + same size
• Similar = same shape only Photographs enlarged or reduced always remain similar.

Answer 1

The Correct Option is B

Concept: In geometry, two figures are said to be similar if:
• their corresponding angles are equal, and
• their corresponding sides are proportional. Similarity means the shape remains exactly the same, although the size may increase or decrease. On the other hand:
• Congruent figures have the same shape and the same size.
• Similar figures have the same shape but may have different sizes.

Step 1: Understand what happens during enlargement or reduction. When a photograph is enlarged:
• every length increases in the same proportion,
• all angles remain unchanged,
• the shape remains identical. Similarly, when a photograph is reduced:
• every length decreases proportionally,
• the overall appearance remains the same,
• only the size changes.

Step 2: Compare with definition of similarity. In enlarged or reduced photographs:
• corresponding angles remain equal,
• corresponding sides remain proportional. Therefore, the photographs satisfy all conditions of similar figures.

Step 3: Explain why they are not congruent. Congruent figures must have: \[ \text{same shape + same size} \] But enlarged or reduced photographs have different sizes. Hence they cannot be congruent.

Step 4: Final conclusion. Since the shape remains the same but the size changes proportionally: \[ \boxed{\text{Reduced and enlarged photographs are similar}} \] Final Answer: \[ \boxed{\text{similar}} \]