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. - PowerPoint PPT Presentation
Transcript of Honors Geometry Section 4.6 Special 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.
*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.
altitude
median
altitude
A
B CM
A midsegment of a triangle is segment joining the midpoints of two sides of a triangle.
Theorem 4.6.9 Midsegment Theorem
A 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:
105w75z4x 5.
542
y
y
2,
22121 yyxx
221
221 yyxx
12
12
xx
yym
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: _______________________
equal
sreciprocal opposite
bmxy
11 xxmyy
a) Find the length of the median from vertex A
AB
C
)5,3(2
28,
2
42
)5,3(
34
53
0503
22
22
b) Write the equation of theline containing the median from vertex A.
)5,3(
11 xxmyy
00 xmy
3
5
03
05
m
03
50 xy
c) Write the equation of theline containing the altitude from vertex A.
)5,3(
?
32
6
42
28
m
reciprocal
opposite
11 xxmyy
00 xmy:BC of Slope
03
10 xy
)5,3(
)1,2(
17
41
1523
22
22
