Question

the following pair of angles with their respective definitions.
∠3 and ∠7
∠2 and ∠7
∠4 and ∠5
∠3 and ∠6
drag & drop the answer
corresponding angles
alternate exterior angles
alternate interior angles

Explanation:

To solve this, we analyze each angle pair using the definitions of corresponding, alternate exterior, and alternate interior angles:

1. $\boldsymbol{\angle 3}$ and $\boldsymbol{\angle 7}$

• Definition of Corresponding Angles: Angles in the same relative position at each intersection where a transversal crosses two lines.
• $\angle 3$ and $\angle 7$ are in the same “corner” position (both below the transversal, to the left of the vertical line), so they are Corresponding Angles.

2. $\boldsymbol{\angle 2}$ and $\boldsymbol{\angle 7}$

• Definition of Alternate Exterior Angles: Angles that lie outside the two lines and on opposite sides of the transversal.
• $\angle 2$ is above the top line (outside the two horizontal lines), $\angle 7$ is below the bottom line (outside the two horizontal lines), and they are on opposite sides of the transversal. Thus, they are Alternate Exterior Angles.

3. $\boldsymbol{\angle 4}$ and $\boldsymbol{\angle 5}$

• Definition of Alternate Interior Angles: Angles that lie between the two lines and on opposite sides of the transversal.
• $\angle 4$ and $\angle 5$ are between the two horizontal lines and on opposite sides of the transversal, so they are Alternate Interior Angles.

4. $\boldsymbol{\angle 3}$ and $\boldsymbol{\angle 6}$

• Definition of Alternate Interior Angles: Angles between the two lines, opposite sides of the transversal.
• $\angle 3$ and $\angle 6$ are between the two horizontal lines and on opposite sides of the transversal, so they are Alternate Interior Angles.

Final Pairings:

• $\angle 3$ and $\angle 7$ $

ightarrow$ Corresponding Angles

• $\angle 2$ and $\angle 7$ $

ightarrow$ Alternate Exterior Angles

• $\angle 4$ and $\angle 5$ $

ightarrow$ Alternate Interior Angles

• $\angle 3$ and $\angle 6$ $

ightarrow$ Alternate Interior Angles

(Note: If the task is to match each pair to its definition, use the above reasoning to drag-and-drop each angle pair to the correct category.)

Answer:

To solve this, we analyze each angle pair using the definitions of corresponding, alternate exterior, and alternate interior angles:

1. $\boldsymbol{\angle 3}$ and $\boldsymbol{\angle 7}$

• Definition of Corresponding Angles: Angles in the same relative position at each intersection where a transversal crosses two lines.
• $\angle 3$ and $\angle 7$ are in the same “corner” position (both below the transversal, to the left of the vertical line), so they are Corresponding Angles.

2. $\boldsymbol{\angle 2}$ and $\boldsymbol{\angle 7}$

• Definition of Alternate Exterior Angles: Angles that lie outside the two lines and on opposite sides of the transversal.
• $\angle 2$ is above the top line (outside the two horizontal lines), $\angle 7$ is below the bottom line (outside the two horizontal lines), and they are on opposite sides of the transversal. Thus, they are Alternate Exterior Angles.

3. $\boldsymbol{\angle 4}$ and $\boldsymbol{\angle 5}$

• Definition of Alternate Interior Angles: Angles that lie between the two lines and on opposite sides of the transversal.
• $\angle 4$ and $\angle 5$ are between the two horizontal lines and on opposite sides of the transversal, so they are Alternate Interior Angles.

4. $\boldsymbol{\angle 3}$ and $\boldsymbol{\angle 6}$

• Definition of Alternate Interior Angles: Angles between the two lines, opposite sides of the transversal.
• $\angle 3$ and $\angle 6$ are between the two horizontal lines and on opposite sides of the transversal, so they are Alternate Interior Angles.

Final Pairings:

• $\angle 3$ and $\angle 7$ $

ightarrow$ Corresponding Angles

• $\angle 2$ and $\angle 7$ $

ightarrow$ Alternate Exterior Angles

• $\angle 4$ and $\angle 5$ $

ightarrow$ Alternate Interior Angles

• $\angle 3$ and $\angle 6$ $

ightarrow$ Alternate Interior Angles

(Note: If the task is to match each pair to its definition, use the above reasoning to drag-and-drop each angle pair to the correct category.)