Download Geometry – Special Segments in Triangles Perpendicular Bisector

Geometry – Special Segments in Triangles
Passes through
a vertex of the
triangle
Divides a side of
the triangle into
two congruent
parts
Perpendicular
to a side of the
triangle (or to
the line
containing the
side)
A sketch of all
three of the
segments
named in the
single triangle
shown
Divides an
angle into two
congruent parts
The name of the
point of
concurrency
when all 3
segments are
drawn
A
Perpendicular
Bisector
B
C
A
Angle
Bisector
B
C
A
Median
B
C
A
Altitude
B
C
Step 1: Place the word “YES” or “NO” in each cell in the first 4 columns, indicating whether the special segment has the characteristic
described.
Step 2: Use a ruler to sketch all 3 of the special segment named on ∆ABC . Use appropriate geometric “tick marks”, “arc marks”, and
right angle marks to emphasize the characteristics.
Step 3: In the last column of the table, identify the geometric name given to the point of concurrency of each special segment.
Step 4: Based on the markings each triangle shown, identify the special segment by it appropriate name, then write that name in the blank
below the diagram.
A. __________________
B. __________________
C. __________________
D. __________________
Step 5: Circle the name of special segment(s) that have the characteristics described in each statement below. More than one may apply!
1) The point of concurrency can occur inside, outside, or on the triangle. PERPENDICULAR BISECTOR, ANGLE BISECTOR,
MEDIAN, ALTITUDE
2) The segments create 90º angles with sides (right angles). PERPENDICULAR BISECTOR, ANGLE BISECTOR, MEDIAN,
ALTITUDE
3) The distance from the point of concurrency to the vertex is 2/3 the length of the entire special segment. The distance from the
point of concurrency to the side of the triangle is 1/3 the length of the entire special segment. PERPENDICULAR BISECTOR,
ANGLE BISECTOR, MEDIAN, ALTITUDE
4) The point of concurrency always occurs inside the triangle. PERPENDICULAR BISECTOR, ANGLE BISECTOR, MEDIAN,
ALTITUDE
5) The segments drawn from the point of concurrency to each vertex are congruent. PERPENDICULAR BISECTOR,
ANGLE BISECTOR, MEDIAN, ALTITUDE
6) The segments have endpoints at a vertex of a triangle and at the midpoint of the opposite side. PERPENDICULAR BISECTOR,
ANGLE BISECTOR, MEDIAN, ALTITUDE
7) The segments drawn from the point of concurrency, perpendicular to each of the sides, are congruent. PERPENDICULAR BISECTOR,
ANGLE BISECTOR, MEDIAN, ALTITUDE
8) The point of concurrency is the center of gravity. PERPENDICULAR BISECTOR, ANGLE BISECTOR, MEDIAN, ALTITUDE
9) The segments are used when calculating the area of a triangle. PERPENDICULAR BISECTOR, ANGLE BISECTOR, MEDIAN,
ALTITUDE