Questions: Lesson 6: Connecting Similarity and Transformations Cool Down: Forward and Backwards? Determine if each statement must be true, could possibly be true, or definitely can't be true. Explain or show your reasoning. 1. Congruent figures are similar. 2. Similar figures are congruent.

Lesson 6: Connecting Similarity and Transformations Cool Down: Forward and Backwards? Determine if each statement must be true, could possibly be true, or definitely can't be true. Explain or show your reasoning. 1. Congruent figures are similar. 2. Similar figures are congruent.
Transcript text: Lesson 6: Connecting Similarity and Transformations Cool Down: Forward and Backwards? Determine if each statement must be true, could possibly be true, or definitely can't be true. Explain or show your reasoning. 1. Congruent figures are similar. 2. Similar figures are congruent.
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Solution

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Solution Steps

Step 1: Analyze the first statement

The first statement is: "Congruent figures are similar."

  • Congruent figures have the same shape and size.
  • Similar figures have the same shape but not necessarily the same size.
  • Since congruent figures have the same shape, they are also similar.
  • Therefore, the statement must be true.
Step 2: Analyze the second statement

The second statement is: "Similar figures are congruent."

  • Similar figures have the same shape but not necessarily the same size.
  • Congruent figures must have the same shape and size.
  • Similar figures can be congruent only if they also have the same size, but this is not always the case.
  • Therefore, the statement could possibly be true but is not always true.
Step 3: Stop after answering the first two statements

The question contains more than two statements, but according to the guidelines, only the first two are addressed. The remaining statements are left unanswered.

Final Answer

  1. The first statement must be true: \( \boxed{\text{must be true}} \)
  2. The second statement could possibly be true: \( \boxed{\text{could possibly be true}} \)
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