Question
"The quadrilaterals have four pairs of congruent corresponding angles, so the figures are similar." What error did Konnor make in his conclusion? Choose 1 answer: (A) The quadrilaterals are congruent, not similar. (B) It's impossible to map STUV onto WXYZ using only rigid transformations and dilations, so the figures are not similar.
Ask by Vega Rojas. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Konnor assumed that having four pairs of congruent corresponding angles is enough to make the quadrilaterals similar. However, similarity also requires that the corresponding sides are in proportion. Since Konnor didn't check if the sides are proportional, his conclusion that the quadrilaterals are similar is incorrect.
Solution
Konnor made an error in his conclusion by assuming that having four pairs of congruent corresponding angles is sufficient to declare the quadrilaterals similar. However, similarity between figures requires not only that all corresponding angles are congruent but also that the corresponding sides are in proportion.
**Correct Answer:**
**(B) It's impossible to map STUV onto WXYZ using only rigid transformations and dilations, so the figures are not similar.**
This option correctly identifies that similarity requires more than just angle congruence; it also requires that the sides are proportional, which Konnor did not verify. Therefore, his conclusion that the quadrilaterals are similar is incorrect because the necessary condition of proportional sides was not met.
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Simplify this solution Mind Expander
Konnor's conclusion contains a flaw because having four pairs of congruent angles in quadrilaterals indicates that the figures are similar; however, not all similar quadrilaterals are congruent. They can have different sizes while maintaining the same shape. This means Konnor may have confused similarity with congruence, which is a common misconception in geometry. A quick tip: Always remember that two figures can be similar (same shape, different size) or congruent (same shape and size). When angles are preserved but the sides differ in length, the figures are similar but not congruent. It's crucial to differentiate between these concepts to avoid confusion!
