Notes for 3.2

<H1>Notes for 3.2</H1>
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**I. Key Concepts & Theorems:**

**Corresponding Angles Theorem:**
When a transversal intersects two parallel lines, corresponding angles are congruent (equal). This means angles in the same relative position at each intersection are equal. Example: Angles A and B (as shown in the recording) are corresponding angles and are congruent.

**Supplementary Angles Theorem:**
When a transversal intersects two parallel lines, consecutive interior angles (angles on the same side of the transversal and inside the parallel lines) are supplementary. This means their sum is 180 degrees. Example: Angles A and B (in a different configuration than the corresponding angles example) are supplementary; C and D are also supplementary.

**Vertical Angles Theorem:**
When two lines intersect, vertical angles (angles opposite each other) are congruent. Example: Angles A and B (in the context of intersecting lines, not parallel lines and a transversal) are vertical angles and are congruent; C and D are also vertical angles and congruent.

**Alternate Interior Angles Theorem:**
When a transversal intersects two parallel lines, alternate interior angles (angles on opposite sides of the transversal and inside the parallel lines) are congruent. Example: Angles A and B (in the context of alternate interior angles) are congruent; C and D are also congruent.

**Alternate Exterior Angles Theorem:**
When a transversal intersects two parallel lines, alternate exterior angles (angles on opposite sides of the transversal and outside the parallel lines) are congruent. Example: Angles A and B (in the context of alternate exterior angles) are congruent; C and D are also congruent.

**II. Vocabulary:**

**Transversal:** A line that intersects two or more other lines.
Parallel Lines: Lines that never intersect.

**Corresponding Angles:** Angles in the same relative position at each intersection of transversal and parallel lines.

**Supplementary Angles:** Two angles whose sum is 180 degrees.
Congruent Angles: Angles that have the same measure.

**Vertical Angles:** Angles opposite each other when two lines intersect.

**Alternate Interior Angles:** Angles on opposite sides of the transversal and inside the parallel lines.

**Alternate Exterior Angles:** Angles on opposite sides of the transversal and outside the parallel lines.