triangles triangles exploration activity topic: medians
TRANSCRIPT
Triangles Triangles
Exploration Activity
Exploration Activity
Topic: Medians
Topic: Medians
QuestionQuestion
to to
Answer Answer
What is a median?
What is a median?A line segment that joins
A line segment that joins
the vertex of a triangle
the vertex of a triangle
to the midpoint of its
to the midpoint of its
opposite side.
opposite side.
QuestionQuestion
to to
Answer Answer
How many medians are
How many medians are
in a triangle?
in a triangle?ThreeThree
CONCEPTS CONCEPTS TO KNOWTO KNOW• All medians meet at a
All medians meet at a
common point called a
common point called a
CENTROIDCENTROID..
• The The centroidcentroid always
always
lie in the interior of the
lie in the interior of the
triangle.triangle.
Statement to Explore
Statement to Explore
Medians of a triangle
Medians of a triangle
concurconcur..
EXPLORATION ACTIVIYEXPLORATION ACTIVIY
Objectives:Objectives:
To verify medians of a triangle concur at a point called a centroid, always lie in the interior of the triangle, by
paper folding.
To discover the property involving the segment lengths
of medians by measuring segment parts with a ruler.
MATERIALS NEEDED:MATERIALS NEEDED:
COLORED PAPERCOLORED PAPER
SCISSORSSCISSORS
RULERRULER
MARKER OR COLORING PENCILMARKER OR COLORING PENCIL
PAPER AND PENCIL TO RECORD FINDINGSPAPER AND PENCIL TO RECORD FINDINGS
STEP 1
STEP 1
Take a colored paper and draw any triangle ABC. Cut the triangle.
STEP 2STEP 2
To get the mid point of BC, fold along BC, such that, point B coincides with
C .
STEP 3STEP 3
Unfold and mark the mid point of BC as M.
STEP 4
STEP 4
Form a crease joining AM.
NOTE: AM is a median.
STEP 5STEP 5
Similarly get medians BN and CP by paper folding. In your groups, discuss what you
observe?
Record your answer on notebook paper.
STEP 6
STEP 6
• Take your ruler and Take your ruler and measure the lengths for measure the lengths for medians AM, BN, and CP. medians AM, BN, and CP. Record the lengths for each Record the lengths for each on your notebook paper.on your notebook paper.
AM = _______AM = _______
BN = _______BN = _______
CP = _______CP = _______
STEP 7
STEP 7
• Mark and label point X as the Mark and label point X as the centroid of your triangle. centroid of your triangle.
• Now, measure and record the Now, measure and record the lengths of both segments of lengths of both segments of each median on your each median on your notebook paper.notebook paper.
AX = _______ XM = _______AX = _______ XM = _______
BX = _______ XN = _______BX = _______ XN = _______
CX = _______ XP = _______CX = _______ XP = _______
CONCLUSIONCONCLUSION
Discuss your findings
Discuss your findings
from the previous slide in
from the previous slide in
your group.your group.
What pattern(s) do you
What pattern(s) do you
see between the see between the
measured lengths of the
measured lengths of the
two segments of the
two segments of the
medians of the triangles?
medians of the triangles?
Between the median
Between the median
and each segment of the
and each segment of the
median?median?
Write your conclusions
on your notebook
paper.
Repeat the
activity if
needed .
ACTIVITY RESULT 1ACTIVITY RESULT 1
Result : It is verified that the medians of a triangle concur at a point called a centroid which always lie in the interior of triangle.
ACTIVITY RESULT
ACTIVITY RESULT
22Result: The centroid divides each
median in the ratio 2:1.
• The segment from the centroid to the
The segment from the centroid to the
midpoint is a third of the length of the
midpoint is a third of the length of the
median.median.
• The segment from the centroid to the
The segment from the centroid to the
vertex is two thirds of the length of
vertex is two thirds of the length of
the median.the median.
Staple your triangle
Staple your triangle
to your notebook
to your notebook
paper. Turn your
paper. Turn your
notebook paper in for
notebook paper in for
a participation grade.
a participation grade.
ACTIVITY LINKACTIVITY LINKhttp://mykhmsmathclass.blogspot.com/2009/08/http://mykhmsmathclass.blogspot.com/2009/08/
activity-medians-of-triangle-concur.htmlactivity-medians-of-triangle-concur.html
This activity can befound on the CMS Secondary This activity can befound on the CMS Secondary WikiWiki
High School High School GeometryGeometry
Unit 3 – Triangles and CongruenceUnit 3 – Triangles and CongruenceSee Resources LinkSee Resources Link
Title: Medians of a Triangle ActivityTitle: Medians of a Triangle Activity