Warm up solve for x
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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.

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Warm up solve for x

Warm up: Solve for x.

Linear Pair

4x + 3

7x + 12

X = 15


Special segments in triangles

Special Segments in Triangles


Median

Median

Connect vertex to

opposite side's

midpoint


Altitude

Altitude

Connect vertex to

opposite side and is

perpendicular


Warm up solve for x

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

Perpendicular Bisector

Goes through the

midpoint and is

perpendicular


Warm up solve for x

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

NO

NO

YES


Angle bisector

Angle Bisector

Cuts the angle

In to TWO

congruent parts


Start to memorize

Start to memorize…

  • Indicate the special triangle segment based on its description


Warm up solve for x

Who am I?

I cut an angle into two equal parts

Angle Bisector


Warm up solve for x

Who am I?

I connect the vertex to the opposite side’s midpoint

Median


Warm up solve for x

Who am I?

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

Altitude


Warm up solve for x

Who am I?

I go through a side’s midpoint and I am perpendicular

Perpendicular Bisector


Drill practice

Drill & Practice

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


Multiple choice identify the red segment

Multiple ChoiceIdentify the red segment

Q1:

  • Angle BisectorB. Altitude

  • C. MedianD. Perpendicular Bisector


Multiple choice identify the red segment1

Multiple ChoiceIdentify the red segment

Q2:

  • Angle BisectorB. Altitude

  • C. MedianD. Perpendicular Bisector


Multiple choice identify the red segment2

Multiple ChoiceIdentify the red segment

Q3:

  • Angle BisectorB. Altitude

  • C. MedianD. Perpendicular Bisector


Multiple choice identify the red segment3

Multiple ChoiceIdentify the red segment

Q4:

  • Angle BisectorB. Altitude

  • C. MedianD. Perpendicular Bisector


Multiple choice identify the red segment4

Multiple ChoiceIdentify the red segment

Q5:

  • Angle BisectorB. Altitude

  • C. MedianD. Perpendicular Bisector


Multiple choice identify the red segment5

Multiple ChoiceIdentify the red segment

Q6:

  • Angle BisectorB. Altitude

  • C. MedianD. Perpendicular Bisector


Multiple choice identify the red segment6

Multiple ChoiceIdentify the red segment

Q7:

  • Angle BisectorB. Altitude

  • C. MedianD. Perpendicular Bisector


Multiple choice identify the red segment7

Multiple ChoiceIdentify the red segment

Q8:

  • Angle BisectorB. Altitude

  • C. MedianD. Perpendicular Bisector


Points of concurrency

Points of Concurrency


New vocabulary points of intersection

New Vocabulary(Points of Intersection)

Centroid

Orthocenter

Incenter

Circumcenter


Point of intersection

Point of Intersection

Medians

intersect at the

centroid


Important info about 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.


Warm up solve for x

The intersection of the medians is called the CENTROID.


Point of intersection1

Point of Intersection

Altitudes

intersect at the

orthocenter


Important info about 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.


Warm up solve for x

The intersection of the altitudes is called the ORTHOCENTER.


Point of intersection2

Point of Intersection

Angle Bisector

intersect at the

incenter


Important info about 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


Warm up solve for x

The intersection of the angle bisectors is called the INCENTER.


Point of intersection3

Point of Intersection

Perpendicular Bisectors

intersect at the

circumcenter


Important information about 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.


Warm up solve for x

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

Memorize these!


Will this work

MC

AO

ABI

PBCC

My Cousin

Ate Our

Avocados But I

Prefer Burritos Covered in Cheese

Will this work?


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