Question

given the information below, match the following items.

given statement: if two angles add to 90°, then they are complementary.

1. converse

☐ if two angles are not complementary, then they do not add to 90°.
☐ if two angles are complementary, then they add to 90°.
☐ if two angles do not add to 90°, then they are not complementary.

1. inverse
2. contrapositive

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Explanation:

Let the original statement be \( p \to q \), where \( p \): "two angles add to \( 90^\circ \)" and \( q \): "they are complementary".

Step 1: Recall Definitions

• Converse: \( q \to p \) (swap hypothesis and conclusion).
• Inverse: \(

eg p \to
eg q \) (negate both hypothesis and conclusion).

• Contrapositive: \(

eg q \to
eg p \) (negate and swap hypothesis and conclusion).

Step 2: Analyze Each Statement

1. For "converse": We need \( q \to p \), which is "If two angles are complementary, then they add to \( 90^\circ \)".
2. For "inverse": We need \(

eg p \to
eg q \), which is "If two angles do not add to \( 90^\circ \), then they are not complementary".

1. For "contrapositive": We need \(

eg q \to
eg p \), which is "If two angles are not complementary, then they do not add to \( 90^\circ \)".

Answer:

1. converse - If two angles are complementary, then they add to \( 90^\circ \).
2. inverse - If two angles do not add to \( 90^\circ \), then they are not complementary.
3. contrapositive - If two angles are not complementary, then they do not add to \( 90^\circ \).