Warm up: Solve for x. Linear Pair 4x + 3 7x + 12 X = 15

Special Segments in Triangles

Median Connect vertex to opposite side's midpoint

Altitude Connect vertex to opposite side and is perpendicular

The altitude is the “true height” of the triangle. Tell whether each red segment is an altitude of the triangle. The altitude is the “true height” of the triangle. YES NO YES

Perpendicular Bisector Goes through the midpoint and is perpendicular

Tell whether each red segment is an perpendicular bisector of the triangle. NO NO YES

Angle Bisector Cuts the angle In to TWO congruent parts

Start to memorize… Indicate the special triangle segment based on its description

I cut an angle into two equal parts Who am I? I cut an angle into two equal parts Angle Bisector

I connect the vertex to the opposite side’s midpoint Who am I? I connect the vertex to the opposite side’s midpoint Median

I connect the vertex to the opposite side and I’m perpendicular Who am I? I connect the vertex to the opposite side and I’m perpendicular Altitude

Perpendicular Bisector Who am I? I go through a side’s midpoint and I am perpendicular Perpendicular Bisector

Drill & Practice Indicate which special triangle segment the red line is based on the picture and markings

Multiple Choice Identify the red segment Q1: Angle Bisector B. Altitude C. Median D. Perpendicular Bisector

Multiple Choice Identify the red segment Q2: Angle Bisector B. Altitude C. Median D. Perpendicular Bisector

Multiple Choice Identify the red segment Q3: Angle Bisector B. Altitude C. Median D. Perpendicular Bisector

Multiple Choice Identify the red segment Q4: Angle Bisector B. Altitude C. Median D. Perpendicular Bisector

Multiple Choice Identify the red segment Q5: Angle Bisector B. Altitude C. Median D. Perpendicular Bisector

Multiple Choice Identify the red segment Q6: Angle Bisector B. Altitude C. Median D. Perpendicular Bisector

Multiple Choice Identify the red segment Q7: Angle Bisector B. Altitude C. Median D. Perpendicular Bisector

Multiple Choice Identify the red segment Q8: Angle Bisector B. Altitude C. Median D. Perpendicular Bisector

Points of Concurrency

New Vocabulary (Points of Intersection) Centroid Orthocenter Incenter Circumcenter

Point of Intersection Medians intersect at the centroid

Important Info about the Centroid The intersection of the medians. Found when you draw a segment from one vertex of the triangle to the midpoint of the opposite side. The center is two-thirds of the distance from each vertex to the midpoint of the opposite side. Centroid always lies inside the triangle. This is the point of balance for the triangle.

The intersection of the medians is called the CENTROID.

Altitudes orthocenter Point of Intersection Altitudes intersect at the orthocenter

Important Info about the Orthocenter This is the intersection point of the altitudes. You find this by drawing the altitudes which is created by a vertex connected to the opposite side so that it is perpendicular to that side. Orthocenter can lie inside (acute), on (right), or outside (obtuse) of a triangle.

The intersection of the altitudes is called the ORTHOCENTER.

Angle Bisector incenter Point of Intersection Angle Bisector intersect at the incenter

Important Info about the Incenter The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle. Incenter is equidistant from the sides of the triangle. The center of the triangle’s inscribed circle. Incenter always lies inside the triangle

The intersection of the angle bisectors is called the INCENTER.

Perpendicular Bisectors Point of Intersection Perpendicular Bisectors intersect at the circumcenter

Important Information about the Circumcenter The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle. The circumcenter is the center of a circle that surrounds the triangle touching each vertex. Can lie inside an acute triangle, on a right triangle, or outside an obtuse triangle.

The intersection of the perpendicular bisector is called the CIRCUMCENTER.

Memorize these! MC AO ABI PBCC Medians/Centroid Altitudes/Orthocenter Angle Bisectors/Incenter Perpendicular Bisectors/Circumcenter

Will this work? MC AO ABI PBCC My Cousin Ate Our Avocados But I Prefer Burritos Covered in Cheese