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→Concept Map
These points of concurrencies, orthocenter, centroid, and circumcenter of any triangle are collinear that is they lie on the same straight line called the Euler line.
These points of concurrencies, orthocenter, centroid, and circumcenter of any triangle are collinear that is they lie on the same straight line called the Euler line.
=====Activities #=====
======Activities #======
======[[Exploring concurrent lines from given surroundings]]======
======[[Exploring concurrent lines from given surroundings]]======
Interactive activity to introduce concurrent lines using examples from our surroundings.
Interactive activity to introduce concurrent lines using examples from our surroundings.
[[Image:KOER%20Triangles_html_m404a4c0b.gif|link=]]
[[Image:KOER%20Triangles_html_m404a4c0b.gif|link=]]
=====Activities #=====
======Activities #======
======[[Marking centroid of a triangle|Marking centroid of the triangle]]======
======[[Marking centroid of a triangle|Marking centroid of the triangle]]======
This is a hands on activity to explore concurrent lines formed in a triangle when vertices are joined to the midpoints of the opposite side.
This is a hands on activity to explore concurrent lines formed in a triangle when vertices are joined to the midpoints of the opposite side.
=====Concept #: Concurrency of altitudes in triangles=====
=====Concept #: Concurrency of altitudes in triangles=====
The distance between a vertex of a triangle and the opposite side is called the altitude of the triangle. Altitude also refers to the length of the segment. Altitudes can be used to compute the area of a triangle: one half of the product of an altitude's length and its base's length equals the triangle's area. A triangle has 3 altitudes. The intersecting point of 3 altitudes of a triangle is known as orthocentre of the triangle. This point may be inside, outside, or on the triangle. If the triangle is obtuse, it will be outside. If the triangle is acute, the orthocentre is inside the triangle. The orthocenter on a right triangle would be directly on the 90° vertex. From Greek: orthos - "straight, true, correct, regular" The point where the three altitudes of a triangle intersect. One of a triangle's points of concurrency.
The distance between a vertex of a triangle and the opposite side is called the altitude of the triangle. Altitude also refers to the length of the segment. Altitudes can be used to compute the area of a triangle: one half of the product of an altitude's length and its base's length equals the triangle's area. A triangle has 3 altitudes. The intersecting point of 3 altitudes of a triangle is known as orthocentre of the triangle. This point may be inside, outside, or on the triangle. If the triangle is obtuse, it will be outside. If the triangle is acute, the orthocentre is inside the triangle. The orthocenter on a right triangle would be directly on the 90° vertex. From Greek: orthos - "straight, true, correct, regular" The point where the three altitudes of a triangle intersect. One of a triangle's points of concurrency.
=====Activities #=====
======Activities #======
======[[Altitudes and orthocenter of a triangle]]======
======[[Altitudes and orthocenter of a triangle]]======
An altitude of a triangle is a line segment that is drawn from the vertex to the opposite side and is perpendicular to the side. A triangle can have three altitudes. Point of intersection of these lines for different types of triangles is explored.
An altitude of a triangle is a line segment that is drawn from the vertex to the opposite side and is perpendicular to the side. A triangle can have three altitudes. Point of intersection of these lines for different types of triangles is explored.
One consequence of the Perpendicular Bisector Theorem is that the perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle.
One consequence of the Perpendicular Bisector Theorem is that the perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle.
=====Activities #=====
======Activities #======
[[Perpendicular bisectors and circumcenter of a triangle|'''Perpendicular bisectors and circumcenter of a triangle''']]
[[Perpendicular bisectors and circumcenter of a triangle|'''Perpendicular bisectors and circumcenter of a triangle''']]
If a point is on the bisector of an angle, then it is equidistant from the two arms of the angle.
If a point is on the bisector of an angle, then it is equidistant from the two arms of the angle.
=====Activities #=====
======Activities #======
======[[Angular bisectors and incenter of a triangle]]======
======[[Angular bisectors and incenter of a triangle]]======
The intersecting point of three lines which are the bisectors of three angles of a triangle that is the incenter and it's properties are examined.
The intersecting point of three lines which are the bisectors of three angles of a triangle that is the incenter and it's properties are examined.