question 9 of 40

if a right triangle $\delta def$ is dilated by a scale factor of 2, which of the following statements is not true?

a. the sides of $\delta def$ are congruent to the sides of $\delta def$.
b. $\delta def$ is larger than $\delta def$.
c. $\delta def$ is similar to $\delta def$.
d. the angles of $\delta def$ are congruent to the angles of $\delta def$.

Question

question 9 of 40

if a right triangle $\delta def$ is dilated by a scale factor of 2, which of the following statements is not true?

a. the sides of $\delta def$ are congruent to the sides of $\delta def$.
b. $\delta def$ is larger than $\delta def$.
c. $\delta def$ is similar to $\delta def$.
d. the angles of $\delta def$ are congruent to the angles of $\delta def$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Scale Factor", "Similar Triangles" ], "new_concepts": [ "Geometric Dilation Properties" ], "current_concepts": [ "Scale Factor", "Similar Triangles", "Geometric Dilation Properties" ] } ## Analyze properties of dilation $$ \begin{aligned} &\text{Dilation by scale factor } k = 2 \implies \text{Side lengths are multiplied by } 2.\ &\text{Since } k e 1, \text{ corresponding sides are not congruent: } s' = 2s e s. \end{aligned} $$ ## Evaluate the given statements $$ \begin{aligned} &\text{A. Sides are congruent: False (since } s' = 2s).\ &\text{B. } \triangle D'E'F' \text{ is larger: True (scale factor } 2 > 1).\ &\text{C. Triangles are similar: True (dilation preserves shape/similarity)}.\ &\text{D. Angles are congruent: True (dilation preserves angle measures)}. \end{aligned} $$ ## Identify the false statement $$ \text{Statement A is not true.} $$

A. The sides of $\triangle DEF$ are congruent to the sides of $\triangle D'E'F'$.

B. $\triangle D'E'F'$ is larger than $\triangle DEF$.

C. $\triangle DEF$ is similar to $\triangle D'E'F'$.

D. The angles of $\triangle DEF$ are congruent to the angles of $\triangle D'E'F'$.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Geometric Dilation Properties" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze properties of dilation

Evaluate the given statements

Identify the false statement

Answer: