An angle is formed when two rays meet

at a common endpoint called the VERTEX

Measured in DEGREES (°)

A line extends INFINITELY in both directions

Has NO endpoints

Named with two points: Line AB or AB with arrows ↔

A line segment has a DEFINITE length

Has TWO endpoints

Named with two points: Segment AB or AB with bar —

A ray starts at ONE point and extends infinitely

Has ONE endpoint (starting point)

Named with two points: Ray AB or AB with arrow →

Lines that NEVER intersect

Always the SAME distance apart

Symbol: AB || CD (line AB is parallel to line CD)

Lines that intersect at a RIGHT ANGLE (90°)

Form four right angles at intersection

Symbol: AB ⊥ CD (line AB is perpendicular to line CD)

Lines that cross at ONE point

Can intersect at any angle

If they intersect at 90°, they are perpendicular

∠A + ∠B = 90°

Two angles whose measures ADD UP to 90°

Example:

∠A + ∠B = 180°

Two angles whose measures ADD UP to 180°

Example:

For Complementary: Missing angle = 90° − given angle

For Supplementary: Missing angle = 180° − given angle

Vertical angles are formed when two lines intersect

They are OPPOSITE each other

They are ALWAYS EQUAL

∠1 = ∠3

∠2 = ∠4

Vertical angles are congruent (equal)

Adjacent angles share a COMMON VERTEX

and a COMMON SIDE

They are NEXT TO each other

They do NOT overlap

Example:

A transversal is a line that intersects

TWO or more lines at different points

1. Corresponding Angles

2. Alternate Interior Angles

3. Alternate Exterior Angles

4. Consecutive Interior Angles (Same-Side Interior)

✓ Corresponding angles are EQUAL

✓ Alternate interior angles are EQUAL

✓ Alternate exterior angles are EQUAL

✓ Consecutive interior angles are SUPPLEMENTARY (180°)

Problem: Two complementary angles. One angle is 2x and the other is 3x. Find both angles.

Problem: Two lines intersect. One angle is 3x + 10 and its vertical angle is 5x − 30. Find x.

Problem: Two parallel lines cut by a transversal. One angle is 4x and its corresponding angle is 100°. Find x.

A line, segment, or ray that divides a segment

into TWO EQUAL parts

If AB is bisected at point M, then AM = MB

A ray that divides an angle

into TWO EQUAL angles

If ray BD bisects ∠ABC, then ∠ABD = ∠DBC

Problem: Ray BD bisects ∠ABC. If ∠ABC = 80°, find ∠ABD.

✓ Complementary: Add to 90° (Think: Corner = 90°)

✓ Supplementary: Add to 180° (Think: Straight line = 180°)

✓ Vertical angles: Always equal when two lines intersect

✓ Adjacent angles: Share a side and vertex, no overlap

✓ Parallel lines (||): Never meet, same distance apart

✓ Perpendicular lines (⊥): Meet at 90°

✓ Corresponding angles: Same position, equal if lines parallel

✓ Alternate interior: Z-pattern, equal if lines parallel

✓ Consecutive interior: Same side, supplementary if lines parallel

✓ Bisector: Divides into two equal parts

Complementary vs Supplementary:

"C comes before S, 90 comes before 180 - Complementary is smaller, Supplementary is greater!"

Vertical Angles:

"Vertical angles are twins - they're always the same, no need to spin!"

Parallel Lines:

"Parallel lines are like train tracks - they never cross, they never lack!"

Alternate Interior (Z-Pattern):

"Draw a Z to see them clear - alternate interior angles are equal, dear!"

Corresponding Angles (F-Pattern):

"Draw an F, you'll quickly see - corresponding angles are equal as can be!"

Bisector:

"Bisector means 'cut in two' - makes two equal parts, through and through!"