COLLEGE OF EDUCATION ARTS,
SCIENCES
MATH MJR 3217 – MODERN GEOMETRY
DIRECTIONS: Classify each statement as TRUE or FALSE. It is FALSE, determine its
proof.
1. The alternate interior angle theorem states that if parallel lines are cut by a transversal,
then alternate interior angles are congruent to each other. TRUE
2. Saccheri-Legendre Theorem can be proven by elliptic geometry. TRUE
3. It is impossible to prove in neutral geometry that quadrilaterals exist. FALSE
PROOF: In neutral geometry, we can prove the existence of triangles, and from
triangles, we can construct quadrilaterals by connecting two triangles together along a
common side. Consider any two triangles with a common side. We can join these
triangles along their common side to form a quadrilateral with four sides. This
construction is valid in neutral geometry because it does not depend on the parallel
postulate.
4. An exterior angle of a triangle is any angle that is not in the interior of the triangle.
TRUE
5. Another way of stating the Saccheri-Legendre theorem is to say that the defect of a
triangle cannot be negative. TRUE
6. According to our definition of "angle," the degree measure of an angle cannot equal
90°. FALSE
PROOF:
SCIENCES
MATH MJR 3217 – MODERN GEOMETRY
DIRECTIONS: Classify each statement as TRUE or FALSE. It is FALSE, determine its
proof.
1. The alternate interior angle theorem states that if parallel lines are cut by a transversal,
then alternate interior angles are congruent to each other. TRUE
2. Saccheri-Legendre Theorem can be proven by elliptic geometry. TRUE
3. It is impossible to prove in neutral geometry that quadrilaterals exist. FALSE
PROOF: In neutral geometry, we can prove the existence of triangles, and from
triangles, we can construct quadrilaterals by connecting two triangles together along a
common side. Consider any two triangles with a common side. We can join these
triangles along their common side to form a quadrilateral with four sides. This
construction is valid in neutral geometry because it does not depend on the parallel
postulate.
4. An exterior angle of a triangle is any angle that is not in the interior of the triangle.
TRUE
5. Another way of stating the Saccheri-Legendre theorem is to say that the defect of a
triangle cannot be negative. TRUE
6. According to our definition of "angle," the degree measure of an angle cannot equal
90°. FALSE
PROOF:
