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Geometry

Points, Lines, and Angles

Lesson

Geometry rests on a few primitive objects: points (locations), lines (extend forever in both directions), and planes (flat surfaces extending forever). Everything else is built from these.

Line, ray, segment

  • Line: zero endpoints. Extends both ways forever.
  • Ray: one endpoint, extends forever the other way.
  • Line segment: two endpoints. Finite length.

Angle classification

  • Acute: less than 90∘90^\circ.
  • Right: exactly 90∘90^\circ.
  • Obtuse: between 90∘90^\circ and 180∘180^\circ.
  • Straight: exactly 180∘180^\circ.

Useful facts

  • Two points determine exactly one line.
  • Three non-collinear points determine exactly one plane.
  • A full rotation is 360∘360^\circ.

How to type your answer

For angle-classification questions, type: 1 acute, 2 right, 3 obtuse, 4 straight. For other questions, type just the number.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

Classify a 45∘ angle\text{Classify a } 45^\circ \text{ angle}

Problem 2

Classify a 90∘ angle\text{Classify a } 90^\circ \text{ angle}

Problem 3

Classify a 135∘ angle\text{Classify a } 135^\circ \text{ angle}

Problem 4

Classify a 180∘ angle\text{Classify a } 180^\circ \text{ angle}

Practice

Standard problems matching the lesson.

Problem 5

Classify a 30∘ angle\text{Classify a } 30^\circ \text{ angle}

Problem 6

Classify a 100∘ angle\text{Classify a } 100^\circ \text{ angle}

Problem 7

Classify a 89∘ angle\text{Classify a } 89^\circ \text{ angle}

Problem 8

Classify a 91∘ angle\text{Classify a } 91^\circ \text{ angle}

Problem 9

Classify a 179∘ angle\text{Classify a } 179^\circ \text{ angle}

Problem 10

Classify a 1∘ angle\text{Classify a } 1^\circ \text{ angle}

Problem 11

How many lines do 2 distinct points determine?\text{How many lines do 2 distinct points determine?}

Problem 12

How many endpoints does a line segment have?\text{How many endpoints does a line segment have?}

Problem 13

How many endpoints does a ray have?\text{How many endpoints does a ray have?}

Problem 14

How many endpoints does a line have?\text{How many endpoints does a line have?}

Problem 15

How many planes do 3 non-collinear points determine?\text{How many planes do 3 non-collinear points determine?}

Problem 16

Degrees in a right angle\text{Degrees in a right angle}

Problem 17

Degrees in a straight angle\text{Degrees in a straight angle}

Problem 18

Degrees in a full rotation\text{Degrees in a full rotation}

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

Classify a 119∘ angle\text{Classify a } 119^\circ \text{ angle}

Problem 20

Classify a 61∘ angle\text{Classify a } 61^\circ \text{ angle}

Problem 21

An angle bisected gives two 35∘ halves. Original?\text{An angle bisected gives two } 35^\circ \text{ halves. Original?}

Problem 22

Two adjacent 45∘ angles form what total?\text{Two adjacent } 45^\circ \text{ angles form what total?}

Problem 23

An angle bisected gives two 22.5∘ halves. Original?\text{An angle bisected gives two } 22.5^\circ \text{ halves. Original?}

Problem 24

Quarter rotation in degrees?\text{Quarter rotation in degrees?}

Problem 25

Half rotation in degrees?\text{Half rotation in degrees?}

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