Information Package / Course Catalogue
Basic Concepts in Geometry
Course Code: MTE524
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 8
Objectives of the Course

To provide students to examine all axiomatic nature of geometry and enable them to comprehend the properties of plane figures

Course Content

Definition of geometry, structure of geometry and geometry usage in real life. Explaining the axiom, undefined concept and theorem. Euclidean and non-Euclidean geometries, the basic axioms of Euclidean geometry. The relationships among points, line and plane concepts. The concept of angle, types of angle, equivalence of angle and equivalence axioms, applications related to angles. The definition of the concept of polygon. The definition of triangle, types of triangle, basic and assistant elements of triangle, equivalence axioms and theorems related to triangles, applications related to equivalences in triangles, similarity theorems related to triangles, applications related to similarity in triangles. To prove the theorems of some geometric concepts such as trapezoid, parallelogram, equilateral quadrilateral, rectangle, square, deltoid. Applications related to quadrilaterals. The concept of circle, theorems and proofs related to angle and length in circle, applications related to angle and length in circle. The properties of objects in space, applications related to area and volume of solid objects

Name of Lecturer(s)
Lec. Serhan ULUSAN
Learning Outcomes
1.Explain and apply definition of geometry, its structure and geometry usage in real life
2.Solve problems related definition of triangle concept, kinds of triangles, basic and assistant elements of triangle, equivalence axioms and theorems about triangles, applications related to equivalences in triangles
3.Solve problems related similar triangles, similarity theorems, applications about similarity on triangles
4.Express relations between concepts of line, plane and point
5.Explain concepts of angle, polygon, triangle, disk and their applications
6.Explain the properties of objects in space, applications related to area and volume of solid objects
Recommended or Required Reading
1.Atatürk, M.K. (1937) Geometri, Türk Dil Kurumu Yayınları, Ankara
2.Stakkestad J.M., Wyant L. (1986) Introduction to Geometry, Academic Press, Orlando
3.Tapan-Broutin, M.S. (2010) Bilgisayar Etkileşimli Geometri Öğretimi, Ezgi Kitabevi Yayınları
Weekly Detailed Course Contents
Week 1 - Theoretical
Definition of geometry, structure of geometry and geometry usage in real life. Explain axiom, undefined concept, theorem. Euclidean and non-Euclidean geometries, basic axioms of Euclidean geometry. The relationships between concept of point, line and plane
Week 2 - Theoretical
The concept of angle, types of angle, equivalence of angle and equivalence axioms, applications related to angles
Week 3 - Theoretical
Definition of triangle concept, , types of triangles, basic and assistant elements of triangle, equivalence axioms and theorems related to triangles, applications related to equivalences in triangles
Week 4 - Theoretical
Basic theorems and applcations related isosceles triangle, equilateral triangle, right-angled triangle
Week 5 - Theoretical
Similar triangles, similarity theorems, applications about similarity on triangles, metric relations on right-angled triangle
Week 6 - Theoretical
I., II. Thales Theorems, bisector theorem, Menelaus Theorem, Ceva Theorem
Week 7 - Theoretical
Definition of poligon concept, proof of related theorems as on quadrangle, parallelogram, equilateral quadrangle, rectangle, square, deltoid, trapezoid, isosceles trapezoid
Week 8 - Theoretical
Applications related quadrangles. (Midterm exam)
Week 9 - Theoretical
Concepts of circle and disk, angle, arc, chord, tangent, theorems and proofs related length on circle and disk, applications related angle and length on circle and disk
Week 10 - Theoretical
Inscribed quadrilateral, calculation on length of circle and arc, tangent quadrangle, common tangent of two circle, power of point according to circle, concept of geometrical place, basic drawings ( as drawing triangle given some elements)
Week 11 - Theoretical
Areas of polygonal regions, areas of polygons, areas of regular polygons, calculations on disk, properties of matters in space, solid matter, prisms, right and oblique prisms
Week 12 - Theoretical
Areas and volumes of prisms, pyramids, areas and volumes of pyramids, applications related prisms and pyramids
Week 13 - Theoretical
Conic, area and volume of conic, cutting pyramids, area and volumes of cutting pyramids, applications related conic and cutting pyramids
Week 14 - Theoretical
Sphere, slice of sphere, concept of sphere cover, their area and volumes, applications related sphere
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%30
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory142370
Individual Work140342
Midterm Examination136238
Final Examination148250
TOTAL WORKLOAD (hours)200
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
OÇ-1
4
2
3
2
3
1
1
OÇ-2
3
1
1
3
2
1
1
OÇ-3
2
1
2
3
1
1
1
OÇ-4
2
1
1
4
1
1
1
OÇ-5
2
2
1
2
2
1
1
OÇ-6
3
2
1
3
3
1
1
Adnan Menderes University - Information Package / Course Catalogue
2026