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# Warm up: Solve for x. PowerPoint PPT Presentation

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.

Warm up: Solve for x.

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Linear Pair

4x + 3

7x + 12

X = 15

### 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.

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

Cuts the angle

In to TWO

congruent parts

### Start to memorize…

• Indicate the special triangle segment based on its description

Who am I?

I cut an angle into two equal parts

Angle Bisector

Who am I?

I connect the vertex to the opposite side’s midpoint

Median

Who am I?

I connect the vertex to the opposite side and I’m perpendicular

Altitude

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 ChoiceIdentify the red segment

Q1:

• Angle BisectorB. Altitude

• C. MedianD. Perpendicular Bisector

### Multiple ChoiceIdentify the red segment

Q2:

• Angle BisectorB. Altitude

• C. MedianD. Perpendicular Bisector

### Multiple ChoiceIdentify the red segment

Q3:

• Angle BisectorB. Altitude

• C. MedianD. Perpendicular Bisector

### Multiple ChoiceIdentify the red segment

Q4:

• Angle BisectorB. Altitude

• C. MedianD. Perpendicular Bisector

### Multiple ChoiceIdentify the red segment

Q5:

• Angle BisectorB. Altitude

• C. MedianD. Perpendicular Bisector

### Multiple ChoiceIdentify the red segment

Q6:

• Angle BisectorB. Altitude

• C. MedianD. Perpendicular Bisector

### Multiple ChoiceIdentify the red segment

Q7:

• Angle BisectorB. Altitude

• C. MedianD. Perpendicular Bisector

### Multiple ChoiceIdentify the red segment

Q8:

• Angle BisectorB. Altitude

• C. MedianD. Perpendicular Bisector

Centroid

Orthocenter

Incenter

Circumcenter

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

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

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.

### 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.

MC

AO

ABI

PBCC

Medians/Centroid

Altitudes/Orthocenter

Angle Bisectors/Incenter

Perpendicular Bisectors/Circumcenter

MC

AO

ABI

PBCC

My Cousin

Ate Our