HGeom - 5.3 Bisectors in Triangles

Honors Geometry
5.3 Bisectors in Triangles

is defined as the point at which the three or more lines intersect.

​Point of Concurrency

is defined as when three or more lines intersect at one point.

Concurrent

Important Vocabulary

Theorem 5-6 - Concurrency of Perpendicular Bisectors Theorem

​What is a CIRCUMCENTER?

​This is created by the THREE perpendicular bisectors.

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​Notice: Each vertex of the triangle is EQUIDISTANT from the circumcenter.

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Why is that?! They are the RADIUS of the outside circle! This outside circle is what we call circumscribed about the triangle.

Finding the Circumcenter

​The perpendicular bisector of OS is colored in purple. The perpendicular bisector of PO is colored in green. Where these two lines intersect is the circumcenter (2, 3).


However, it will not always be this easy!

Finding the Circumcenter: Use the diagram below and watch the video on the next slide.

Steps to Finding Circumcenter:

Fill in the Blank

P is the circumcenter of triangle ABC. Find BC.

Fill in the Blank

P is the circumcenter of triangle ABC. Find AP.

Multiple Choice

D is the circumcenter, find ED

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Theorem 5-7 - Concurrency of Angle Bisectors Theorem

​What is an INCENTER?

​Each dashed line is an ANGLE BISECTOR. It only cuts the ANGLE.

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​They all meet at the INCENTER.

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​Notice: The circle is inside of the triangle, or INSCRIBED.

Multiple Choice

If PX is 5, what is PZ?

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Fill in the Blank

Solve for x (enter just the number).

Acronym to Help You Remember

As we work through Chapter 5, we will learn about other centers of triangles including orthocenters and centroids (***). Here is an acronym to help you remember what center goes with which type of line.


All Of ---- Altitude → Orthocenter ***
My Children ---- Median → Centroid ***
Are Brining In ---- Angle Bisector → Incenter
Peanut Butter Cookies ---- Perpendicular Bisector → Circumcenter

Poll

On a scale of 1 to 5, how confident do you feel about this material? (1 being not confident at all and 5 being extremely confident).

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