Euclidean Geometry vs Spherical Geometry

  Statement: Through two given points there is...
Euclidean: One and only one line.
Spherical: ??

• Two lines
• A circle
• A great circle
• Perpendicular lines

Statement: Two distinct lines intersect and forming...
Euclidean: 1 point and 4 angles.
Spherical: ??

• 2 points and 4 angles
• 4 points and 8 angles
  
• 2 points and 8 angles
• 3 points and 6 angles

Tags

CCSS.HSG.CO.A.1

Statement: Given a line 'l' and a point 'P' not on 'l', there exists...
Euclidean: One and only one line parallel to 'l'.
Spherical: ??

• No parallel line
• 2 parallel lines
• 1 parallel line
• 500 parallel lines

Statement: Through a point not on line 'l', there exists...
Euclidean: One and only one line perpendicular to 'l'.
Spherical: ??

• 4 lines perpendicular to 'l'
• 2 lines perpendicular to 'l'
• 3 lines perpendicular to 'l'
• 1 line perpendicular to 'l'

Statement: The sum of the measure of angles of a triangle is...
Euclidean: 180⁰
Spherical: ??

• 180⁰
• Between 180⁰ and 540⁰
• Less than 180⁰
• Greater than 540⁰

Tags

CCSS.HSG.CO.C.10

CCSS.HSG.SRT.D.10

Statement: A triangle can have...
Euclidean: ??
Spherical: Three obtuse angles.

• 2 obtuse angles
• 1 obtuse angle
• No obtuse angles
• 3 obtuse angles

Tags

CCSS.8.G.A.5

Statement: If a triangle contains a right angle, then...
Euclidean: The other two angles are complimentary.
Spherical: ??

• The other two angles are supplementary.
• The other two angles are non existent
• The other two angles are right angles
• The other two angles can vary.

Tags

CCSS.8.G.A.5

In spherical geometry, a triangle can have more than one right angle.

• True
• False

In spherical geometry, if 2 lines are perpendicular to a third line, then they are parallel.

• True
• False

In spherical geometry, the measures of the angles of an equiangular triangle must be 60⁰

• True
• False