Learn it
Geometry starts with undefined terms: a point (a location), a line (straight, endless in both directions) and a plane (a flat surface that goes on forever). A segment has two endpoints; a ray has one.
Angle pairs to know: complementary (sum 90°), supplementary (sum 180°), a linear pair (adjacent and supplementary) and vertical angles (equal).
An angle bisector splits an angle into two equal angles; a segment’s midpoint splits it into two equal segments.
Worked examples
Example 1
Angles A and B form a linear pair. A = (4x + 10)° and B = (2x + 20)°. Find each angle.
- 4x + 10 + 2x + 20 = 180
- 6x = 150, x = 25
- A = 110°, B = 70°
Answer: 110° and 70°
Example 2
M is the midpoint of segment PQ. PM = 3x − 1 and MQ = x + 7. Find PQ.
- PM = MQ: 3x − 1 = x + 7
- x = 4
- PM = 11, so PQ = 22
Answer: 22
Practice
Try these on paper first, then check your work.
- Complement of 28°
- Ray BD bisects a 76° angle ABC. Angle ABD?
- Vertical angles 5x and 3x + 30. x?
- How many endpoints does a ray have?
Show the answer key
- 62°
- 38°
- 15
- 1