Honors geometry section 4 6 special segments in triangles
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Honors Geometry Section 4.6 Special Segments in Triangles PowerPoint PPT Presentation


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Honors Geometry Section 4.6 Special Segments in Triangles.

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Honors Geometry Section 4.6 Special Segments in Triangles

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Honors geometry section 4 6 special segments in triangles

Honors Geometry Section 4.6Special Segments in Triangles


Honors geometry section 4 6 special segments in triangles

Goals for today’s class:1. Understand what a median, altitude and midsegment of a triangle are.2. Correctly sketch medians and altitudes in a triangle and identify any congruent segments or angles that result.3. Write the equation for the line containing a median or altitude given the coordinates of the vertices of the triangle.


Honors geometry section 4 6 special segments in triangles

*When three or more lines intersect at a single point, the lines are said to be __________ and the point of intersection is called the _________________.

concurrent

point of concurrency


Honors geometry section 4 6 special segments in triangles

*A median of a triangle is a segment from a vertex to the midpoint of the opposite side.The medians of a triangle are concurrent at a point called the ________.

centroid


Honors geometry section 4 6 special segments in triangles

*An altitude of a triangle is a segment from a vertex perpendicular to the line containing the opposite side.We have to say “the line containing the opposite side” instead of “the opposite side” because altitudes sometimes fall outside the triangle


Examples sketch the 3 altitudes for each triangle

Examples: Sketch the 3 altitudes for each triangle.

*The point of concurrency for the lines containing the altitudes is called the orthocenter.


Honors geometry section 4 6 special segments in triangles

While the median and altitude from a particular vertex will normally be different segments, that is not always the case. The median and altitude from the vertex angle of an isosceles triangle will be the same segment.


A midsegment of a triangle is segment joining the midpoints of two sides of a triangle

A midsegment of a triangle is segment joining the midpoints of two sides of a triangle.


Honors geometry section 4 6 special segments in triangles

Theorem 4.6.9Midsegment TheoremA midsegment of a triangle is parallel to the third side and half as long as the third side.


Example find the values of all variables

Example: Find the values of all variables:


Honors geometry section 4 6 special segments in triangles

If two lines are parallel, their slopes are_______.If two lines are perpendicular, their slopes are ___________________Slope-Intercept form of the equation of a line: __________________Point-Slope form of the equation of a line: _______________________


A find the length of the median from vertex a

a) Find the length of the median from vertex A


B write the equation of the line containing the median from vertex a

b) Write the equation of theline containing the median from vertex A.


C write the equation of the line containing the altitude from vertex a

c) Write the equation of theline containing the altitude from vertex A.


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