question 1-16
match the converse, inverse, and contrapositive of the given conditional statement.
if two polygons are similar, then their corresponding side lengths are proportional.

| | converse | inverse | contrapositive |
| --- | --- | --- | --- |
| if the corresponding side lengths of two polygons are not proportional, then the two polygons are not similar. | □ | □ | □ |
| if two polygons are not similar, then their corresponding side lengths are not proportional. | □ | □ | □ |
| if the corresponding side lengths of two polygons are proportional, then the two polygons are similar. | □ | □ | □ |

Question

question 1-16
match the converse, inverse, and contrapositive of the given conditional statement.
if two polygons are similar, then their corresponding side lengths are proportional.

| | converse | inverse | contrapositive |
| --- | --- | --- | --- |
| if the corresponding side lengths of two polygons are not proportional, then the two polygons are not similar. | □ | □ | □ |
| if two polygons are not similar, then their corresponding side lengths are not proportional. | □ | □ | □ |
| if the corresponding side lengths of two polygons are proportional, then the two polygons are similar. | □ | □ | □ |

Accepted Answer

To solve this, we recall the definitions:
- **Converse**: Swap hypothesis and conclusion of the original statement ($p \to q$ becomes $q \to p$).
- **Inverse**: Negate both hypothesis and conclusion ($p \to q$ becomes $
eg p \to
eg q$).
- **Contrapositive**: Swap and negate both ($p \to q$ becomes $
eg q \to
eg p$).

Original statement: *If two polygons are similar ($p$), then their corresponding side lengths are proportional ($q$)* ($p \to q$).

### Analyze each row:
1. **Row 1**: *If the corresponding side lengths of two polygons are not proportional ($
eg q$), then the two polygons are not similar ($
eg p$)* ($
eg q \to
eg p$) → This is the **contrapositive**.
2. **Row 2**: *If two polygons are not similar ($
eg p$), then their corresponding side lengths are not proportional ($
eg q$)* ($
eg p \to
eg q$) → This is the **inverse**.
3. **Row 3**: *If the corresponding side lengths of two polygons are proportional ($q$), then the two polygons are similar ($p$)* ($q \to p$) → This is the **converse**.

### Fill the table:
| Statement                                                                 | converse | inverse | contrapositive |
|--------------------------------------------------------------------------|----------|---------|----------------|
| If the corresponding side lengths of two polygons are not proportional, then the two polygons are not similar. | ☐        | ☐       | ☑              |
| If two polygons are not similar, then their corresponding side lengths are not proportional.                   | ☐        | ☑       | ☐              |
| If the corresponding side lengths of two polygons are proportional, then the two polygons are similar.         | ☑        | ☐       | ☐              |

# Answer:
- First statement (contrapositive): Check the "contrapositive" column.
- Second statement (inverse): Check the "inverse" column.
- Third statement (converse): Check the "converse" column.

(In table form, as above: converse for third row, inverse for second, contrapositive for first.)

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QUESTION IMAGE

Question

Explanation:

Analyze each row:

Fill the table:

Answer:

	converse	inverse	contrapositive
if two polygons are not similar, then their corresponding side lengths are not proportional.	□	□	□
if the corresponding side lengths of two polygons are proportional, then the two polygons are similar.	□	□	□