Lab Manual: Mid-point Theorem - Class 9 PDF Download

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Objective

Prerequisite Knowledge
(i) Concept of angles, triangles and mid-points.
(ii) Concept of corresponding angles: If a transversal cuts two straight lines such that their corresponding angles are equal, then the lines are parallel.

Materials Required
Glazed papers, a pair of scissors, pencil, eraser, gluestick, white sheet.

Procedure

• Draw ∆ABC on the yellow glazed paper of any measurement and paste it on white sheet.
• Find mid-points of the two sides (say AB and AC) of a triangle by paper folding. We obtain D and E as mid-points of AB and AC respectively in 1st triangle.
  
• Draw horizontal line DE. Similarly find mid-point of side BC and name it F as shown in fig. (ii).
  
• Trace the ∆ABC on tracing paper and cut ∆ABC along line DE as shown in fig.(iii).
  
• Paste this cut out of triangle ADE [fig. (iii) ] on ∆ABC of fig. (ii) such that AE coincides with EC and ED lies on CB and point D coincides with F as shown in fig. (iv).
• ∆ADE completely covers ∆EFC.

Observation
We observe that ∆ADE exacdy overlaps ∆EFC.
∴ ∠1 = ∠2 (corresponding angles)
AC is any transversal line intersecting the lines DE and BC.
∴ DE || BC.
By paper folding we observe that, in fig (iv) F, the mid point of BC coincides with D.
∴ DE = FC (As DE superimposes on FC)
or DE = FC = BC/2

Result
Hence, it is verified that the line joining the mid-points of two sides of a triangle is parallel to third side and half of it.

Learning Outcome
Line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it. This is true for all types of triangles like acute-angled triangle, obtuse-angled triangle and right-angled triangle.

Activity Time
Students can verify this theorem in different triangles, e.g., obtuse-angled triangle, right-angled triangle, equilateral triangles, scalene triangles.