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# Honors Geometry Section 4.6 Special Segments in Triangles PowerPoint PPT Presentation

Honors Geometry Section 4.6 Special Segments in Triangles.

Honors Geometry Section 4.6 Special Segments in Triangles

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### Honors Geometry Section 4.6Special 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.

*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

*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

*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.

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

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.

### Example: Find the values of all variables:

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: _______________________