RIESI, Administrators
3,664
edits
Changes
Jump to navigation
Jump to search
Line 1:
Line 1: − + + Line 6:
Line 7: + − + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + − +
Quadrilaterals-Activity-Mid-point theorem (view source)
Revision as of 10:10, 7 November 2019
, 10:10, 7 November 2019→Evaluation at the end of the activity
=== Objectives ===
=== Objectives ===
Demonstrate that the line joining the mid-points of any two sides of a triangle is parallel to the third side and equals to half the third side
# Understand properties of triangles – a segment connecting mid-points of two sides of a triangle will be parallel to the third side and its length will be half of the third side
# Demonstrate that the line joining the mid-points of any two sides of a triangle is parallel to the third side and equals to half the third side
=== Estimated Time ===
=== Estimated Time ===
=== Prerequisites/Instructions, prior preparations, if any ===
=== Prerequisites/Instructions, prior preparations, if any ===
Prior knowledge of point, lines, angles, parallel lines, triangles, and quadrilaterals / parallelograms
=== Materials/ Resources needed ===
=== Materials/ Resources needed ===
Geogebra file
Digital - Computer, Geogebra application, projector. Geogebra file - Mid-point theorem.ggb
Non digital -worksheet and pencil.
=== Process (How to do the activity) ===
=== Process (How to do the activity) ===
Work shee - t
Each group member will construct on her / his notebook, using pencil, scale, protractor, and compass a triangle, with the measures provided
# Students should plot the mid-point of two sides and connect these with a line segment.
## They should measure the length of this segment and length of the third side and check if there is any relationship
## They should measure the angles formed at the two vertices connecting the third side, with the two angles formed on the two mid-points
# Question them if there is any relationship between the two segment lengths and the measures of the two pairs of angles.
## Ask them why these relationships are true across different constructions.
# Prove the theorem
## In △ ABC, D and E are the midpoints of sides AB and AC respectively. D and E are joined.
## Given: AD = DB and AE = EC. To Prove: DE ∥∥ BC and DE = 1/2 BC.
## Construction: Extend line segment DE to F such that DE = EF. Draw segment CF.
## Proof: In △ ADE and △ CFE AE = EC (given)
## ∠AED = ∠CEF (vertically opposite angles)
## DE = EF (construction)
## Hence △ ADE ≅ △ CFE by SAS congruence rule.
### Therefore, ∠ADE = ∠CFE (by CPCT) and ∠DAE = ∠FCE (by CPCT) AD = CF (by CPCT).
# ∠ADE and ∠CFE are alternate interior angles,
# (AB and CF are 2 lines intersected by transversal DF).
# ∠DAE and ∠FCE are alternate interior angles,
# (AB and CF are 2 lines intersected by transversal AC).
## Therefore, AB ∥∥ CF. So - BD ∥∥ CF.
# BD = CF (since AD = BD and it is proved above that AD = CF).
## Thus, BDFC is a parallelogram.
# By the properties of parallelogram, we have DF ∥∥ BC DF = BC DE ∥∥ BC.
## DE = 1/2BC (DE = EF by construction)
=== Evaluation at the end of the activity ===
=== Evaluation at the end of the activity ===
# Would this theorem apply for right angled and obtuse-angled triangles?
[[Category:Quadrilaterals]]
[[Category:Quadrilaterals]]
[[Category:Class 9]]
[[Category:Class 9]]