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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. Tell whether each red segment is an altitude of the triangle. - PowerPoint PPT Presentation
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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 Bisector
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q2:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q3:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q4:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q5:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q6:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q7:
A. Angle Bisector B. AltitudeC. Median D. Perpendicular Bisector
Multiple ChoiceMultiple ChoiceIdentify the red segment
Q8:
A. 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
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