Concurrence Worksheets
What is Concurrence in Geometry? The concept of concurrence or concurrency in geometry says that when more than one lines are passing through the same point, it is called concurrence, and the point through which those lines are passing is known as the point of concurrency. Concurrence is used in many mathematical concepts and is immensely helpful in solving and finding the equations of lines, especially through a point-slope formula. Through the point of concurrency, we can also solve the equations of two lines simultaneously since they are assumed to be lying on the same plane. After solving both those equations simultaneously, we can get the values of the variables of those equations, get a solution set and plot those values on the coordinate grid and get a graphical position of those lines in a vector diagram. Such concepts are often used in the field of civil engineering and construction works. It is also used to solve complex vector calculations.
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Basic Lesson
Guides students through finding Concurrence. In triangle ABC, three red lines AD, BE and CF bisects three opposite sides of the triangle, these lines are called as medians. The point O at which all medians are concurrent is called centroid. Centroid is always inside the triangle. It divides the medians into a 2:1 ratio. The section of the median nearest the vertex is twice as long as the section nears the midpoint of the triangle's side.
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Intermediate Lesson
In triangle ABC, three red lines AD, BE and CF are bisects angles BAC, ABC and ACB of the triangle, these lines are called as angle bisectors. The point O at which all angle bisectors are concurrent is called incenter. Incenter is the center of an inscribed circle within the triangle. It is always inside the triangle.
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Independent Practice 1
A really great activity for allowing students to understand the concepts of the Concurrence. Sample: An isosceles triangle ABC, the distance from the centroid of a triangle to the circumcenter is 6 units. How far is the centroid from the orthocenter?
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Independent Practice 2
Students determine the Concurrence in 20 assorted problems. The answers can be found below. Example: Is it possible to locate the centroid of every triangle?
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Homework Worksheet
Students are provided with 12 problems to achieve the concepts of Concurrence.
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Intermediate Lesson
Demonstrates how to use advanced skills to tackle Concurrence problems.
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Independent Practice 1
A really great activity for allowing students to understand the concepts of the Concurrence. Third median always passes through the same point as the other two median?
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Independent Practice 2
Students use Concurrence in 20 assorted problems. The answers can be found below.
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Homework Worksheet
Students are provided with 12 problems to achieve the concepts of Concurrence.
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Full Degrees
If an equilateral triangle were joined by an isosceles triangle
(with two interior angles measuring at 50 degrees). What is the third angle
of the isosceles plus the angle of the equilateral triangle? Answer:
Equilateral is 60,60,60
Isosceles is 50,50,80
60+80=140 degrees