Warm up: Solve for x.Warm up: Solve for x.

Linear Pair

4x + 3 7x + 12

X = 15

Special Special Segments in Segments in

TrianglesTriangles

MedianMedian

AltitudeAltitude

Tell whether each red segment is an altitude of the triangle.

The altitude is the “true

height” of the triangle.

Perpendicular Perpendicular BisectorBisector

Tell whether each red segment is an perpendicular bisector of the triangle.

Angle BisectorAngle Bisector

Start to Start to memorizememorize…

•Indicate the special triangle segment based on its description

I cut an angle into two equal parts

I connect the vertex to the opposite side’s

midpoint

I connect the vertex to the opposite side and

I’m perpendicular

I go through a side’s midpoint and I am

perpendicular

Drill & PracticeDrill & Practice

•Indicate which special triangle segment the red line is based on the picture and markings

Multiple ChoiceMultiple ChoiceIdentify the red segment

Q1:

A. Angle Bisector B. AltitudeC. Median D. Perpendicular BisectorA. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector

Multiple ChoiceMultiple ChoiceIdentify the red segment

Q2:

A. Angle Bisector B. AltitudeC. Median D. Perpendicular BisectorA. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector

Multiple ChoiceMultiple ChoiceIdentify the red segment

Q3:

A. Angle Bisector B. AltitudeC. Median D. Perpendicular BisectorA. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector

Multiple ChoiceMultiple ChoiceIdentify the red segment

Q4:

A. Angle Bisector B. AltitudeC. Median D. Perpendicular BisectorA. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector

Multiple ChoiceMultiple ChoiceIdentify the red segment

Q5:

A. Angle Bisector B. AltitudeC. Median D. Perpendicular BisectorA. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector

Multiple ChoiceMultiple ChoiceIdentify the red segment

Q6:

A. Angle Bisector B. AltitudeC. Median D. Perpendicular BisectorA. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector

Multiple ChoiceMultiple ChoiceIdentify the red segment

Q7:

A. Angle Bisector B. AltitudeC. Median D. Perpendicular BisectorA. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector

Multiple ChoiceMultiple ChoiceIdentify the red segment

Q8:

A. Angle Bisector B. AltitudeC. Median D. Perpendicular BisectorA. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector

Points of Points of ConcurrencyConcurrency

New VocabularyNew Vocabulary(Points of (Points of

Intersection)Intersection)1. Centroid2. Orthocenter3. Incenter4. Circumcenter

Point of Point of IntersectionIntersection

intersect at the

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.

Point of Point of IntersectionIntersection

intersect at the

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.

Point of Point of IntersectionIntersection

intersect at the

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.

Point of Point of IntersectionIntersection

intersect at the

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!Memorize these!

MCAOABI

PBCC

Medians/Centroid

Altitudes/Orthocenter

Angle Bisectors/Incenter

Perpendicular Bisectors/Circumcenter

Will this work?Will this work?

MCAOABI

PBCC

My Cousin

Ate Our

Avocados But I

Prefer Burritos Covered in Cheese