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Learning by Doing

Objective: To verify the property of exterior angle of a triangle. (An exterior angle
of a triangle is equal to the sum of the its interior opposite angles.)
Materials Required: A4 paper sheet, different coloured sketch pens, a pair of
scissors
Procedure: A
• Take a A4 paper sheet and draw a triangle ABC. Extend the side BC ∠1
to point D.
• Mark all the angles as ∠1, ∠2, ∠3, and ∠4 respectively and colour
them by using different colour sketch pens as shown in the adjacent ∠2 ∠3 ∠4
figure. B C D
• Cut off all the angles ∠1, ∠2, ∠3, and ∠4 as shown in the figure given below.

A
∠1
∠1

∠2 ∠4
∠2 ∠3 ∠4 ∠3
B C D
• Place the ∠1 and ∠2 over the ∠4 and try to fit as shown in the figure.

Clearly, the arms of the combination of angles ∠1 and ∠2 overlap the arms of ∠1 ∠4
∠4 completely. Thus, ∠4 = ∠1 + ∠2 ∠2
Hence, an exterior angle of a triangle is equal to the sum of its interior opposite angles.

maths fun

Solve the given crossword puzzle using the given clues. 5
Across
1. A triangle with all its sides unequal.
2. The longest side of a right-angled triangle. 6
1
3. Two triangles having same side lengths. 2 7
4. Line segment drawn from a vertex of a triangle
perpendicular to its opposite side.
Down 3
8
5. Type of the larger angle of a triangle in which altitude 4
falls outside the triangle.
6. A line segment joining vertex with the mid-point of the
opposite side.
7. A regular triangle.
8. In a parallelogram, the line segment that divides it into
two congruent triangles.

195 The Triangle and Its Properties