Why are angle bisectors of a triangle concurrent

If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy. See our Privacy Policy and User Agreement for details. Angle bisectors of internal angle of a triangle are concurrent. The SlideShare family just got bigger. Home Explore Login Signup. Successfully reported this slideshow. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads.

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Show related SlideShares at end. WordPress Shortcode. Next SlideShares. Do you know what this special point is known as and how do you find it? This special point is the point of concurrency of medians. Lesson Plan 1. What Is the Point of Concurrency?

Important Notes on the Point of Concurrency 3. Solved Examples on the Point of Concurrency 4. Challenging Questions on the Point of Concurrency 5. Interactive Questions on the Point of Concurrency. Triangle Concurrency Points Four different types of line segments can be drawn for a triangle. Please refer to the following table for the above statement: Name of the line segment Description Example Perpendicular Bisector These are the perpendicular lines drawn to the sides of the triangle.

Angle Bisector These lines bisect the angles of the triangle. Median These line segments connect any vertex of the triangle to the mid-point of the opposite side. Altitude These are the perpendicular lines drawn to the opposite side from the vertices of the triangle. The different points of concurrency in the triangle are: Circumcenter.

Circumcenter The circumcenter is the point of concurrency of the perpendicular bisectors of all the sides of a triangle.

For an obtuse-angled triangle, the circumcenter lies outside the triangle. For a right-angled triangle, the circumcenter lies at the hypotenuse. Incenter The incenter is the point of concurrency of the angle bisectors of all the interior angles of the triangle.

The incenter always lies within the triangle. The circle that is drawn taking the incenter as the center, is known as the incircle. Centroid The point where three medians of the triangle meet is known as the centroid. Centroid always lies within the triangle.

It always divides each median into segments in the ratio of Orthocenter The point where three altitudes of the triangle meet is known as the orthocenter. For an obtuse-angled triangle, the orthocenter lies outside the triangle.

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