Basic Terms in Geometry
Line segment – a part of a line, bound by two endpoints. It has a definite length.
Note: a line segment has 2 endpoints, but contains an infinite number of points.
Ray – a part of a line starting from one point, stretching or extending infinitely in one direction only.
Line – a geometric figure formed by two opposite rays. In other words, it is extended infinitely in two opposite directions.
[Note: The Line segment, ray and line contain an infinite number of points.]
Two lines may either intersect or not. Two lines that do not intersect are called parallel lines.
Two intersecting lines that form 90o angles are called perpendicular lines.
Angle – a geometric figure formed by two rays with a common endpoint called the vertex.
o Acute angles measure greater than 0 deg but less than 90 deg
o Right angles measure exactly 90 deg
o Obtuse angles measure greater than 90 deg but less than 180 deg
o Reflex angles measure greater than 180 deg but less than 360 deg
Plane – a flat geometric figure extended infinitely in all directions.
Polygon – enclosed figure bound by line segments
3 sides: TRIANGLE
4 sides: QUADRILATERAL
5 sides: PENTAGON
6 sides: HEXAGON
7 sides: HEPTAGON SEPTember
8 sides: OCTAGON OCTober
9 sides: NONAGON NOvember
10 sides: DECAGON DECember
CENTROID
1. All three medians of the triangle will meet at exactly one point, which is the centroid.
2. You may find the incenter using only two angle medians of a triangle.
3. Regardless of the angles of a triangle, the centroid will always be found inside the triangle. This is due to the fact that the medians will always be inside the triangle as well.
4. The centroid divides each median into two segments in the ratio 2:1. This can be checked using the compass.
CIRCUMCENTER
1. The three perpendicular bisectors will always intersect at only one point called the circumcenter.
2. The circumcenter of a triangle will not always be inside the triangle. It will be found inside if the triangle is acute, on the hypotenuse if right, and outside the triangle (particularly behind the longest side) if obtuse.
3. If the triangle is right, then the hypotenuse will be shown as a diameter of the circumcircle. In this case, the midpoint of the hypotenuse will be center of the circumcircle, or circumcenter.
4. The circumcenter is always equidistant to the vertices of the triangle, but not to the sides.
5. Three pairs of congruent triangles will be formed by the sides, the segments formed by the midpoint of each side and the circumcenter, and the segments from the vertices to the circumcenter. These pairs of congruent triangles will share a common side (or leg). The hypotenuse of all six triangles formed are congruent.
INCENTER
1. All three angle bisectors of the triangle will meet at exactly one point, which is the incenter.
2. You may find the incenter using only two angle bisectors of a triangle.
3. Regardless of the angles of a triangle, the incenter will always be found inside the triangle. This is due to the fact that the angle bisectors will always be inside the triangle as well.
4. The incenter is equidistant to the sides of the triangle, but not to the vertices.
5. When the radii are drawn to each side of the triangle, three pairs of congruent triangles will be formed. These triangles are formed by the sides, the radii and the segments from the incenter to the vertices.
ORTHOCENTER
1. All three altitudes of the triangle meet at exactly one point (the orthocenter).
2. You may find the orthocenter using only two altitudes.
3. The orthocenter is found inside the triangle if the triangle is acute, on the vertex of the right angle if the triangle is right, and behind the obtuse angle if obtuse.
4. If you drew the circumcircle of the triangle, you may see that the orthocenter‘s reflections through the sides of the triangle are actually on the circumcircle.
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