Verify experimentally that the sum of sum of interior angles of a triangle is 180 degree Verify experimentally that Base angles of an isosceles triangle are always equal Verify that the Interior angles of an equilateral triangle are always 60 degree Verify experimentally that the Base angles of an isosceles right angled triangle are 45 degree Verify experimentally that The line joining from vertex of an isosceles triangle to join the mid-point of the base is perpendicular to the base In slide No. 29, In figure ABCD is an equilateral triangle is wrong. Please change into ABD is an equilateral triangle.

1. 6/27/2020 JANAK SINGH SAUD 1

2. Objectives: Students will be able to
• Verify experimentally that the sum of sum of interior angles of a triangle
is 1800
• Verify experimentally that Base angles of an isosceles triangle are always
equal
• Verify that the Interior angles of an equilateral triangle are always 600
• Verify experimentally that the Base angles of an isosceles right angled
triangle are 450
• Verify experimentally that The line joining from vertex of an isosceles
triangle to join the mid-point of the base is perpendicular to the base
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3. Review : Types of a triangle
• A triangle having three equal sides is
called an equilateral triangle
• A triangle having any two sides equal is
called an isosceles triangle
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4. Verification of properties of triangles
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A B
C
A
B C
Sum of interior angles of a triangle
∡BAC + ∡ABC + ∡BCA = ?
Relation of base angles of an isosceles triangle
Relation between ∡ABC and ∡BCA
Relation of interior angles of equilateral triangle
Given AB = BC = CA, then Relation between ∡BAC, ∡ABC and ∡BCA
A
B C

5. Experimental verification of sum of interior angles of a triangle
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https://www.geogebra.org/m/FAhtKpR5
https://www.geogebra.org/m/YqaqaUt3
https://www.geogebra.org/m/qyrXkXRZ

6. EXPERIMENT - 1
• Three triangle of different shapes and sizer are drawn
• Measuring all the interior angles and tabulated :
• Conclusion: the sum of interior angles of a triangle is always 1800
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A
B C
A
B
C
A
B
C
Fig. (i)
Fig. (ii)
Fig. (iii)
Figure ∡𝑩𝑨𝑪 ∡ABC ∡BCA Result
(i) ∡BAC + ∡ABC + ∡BCA =
(ii) ∡BAC + ∡ABC + ∡BCA =
(iii) ∡BAC + ∡ABC + ∡BCA =

7. Base angles of an isosceles triangle
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https://www.geogebra.org/m/zQyvhJZv
https://www.geogebra.org/m/MfzdgSYw

8. Relation of Base angles of an isosceles triangle
• Three isosceles triangles ABC with different base BC are drawn
• Measuring the angles of each triangles and tabulated
• Conclusion: Base angles of an isosceles triangle are always equal.
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EXPERIMENT - 2
A
B C
A
B C
A
B C
Figure ∡𝑩𝑨𝑪 ∡ABC ∡BCA Result
(i)
(ii)
(iii)

9. Interior angles of an equilateral triangle
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https://www.geogebra.org/m/VqjH4BPZ

10. Relation of angles of an equilateral triangle triangle
• Three isosceles triangles ABC with different base BC are drawn
• Measuring the angles of each triangles and tabulated
• Conclusion: Base angles of an isosceles triangle are always equal.
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EXPERIMENT - 3
A
B C
A
B C
A
B
C
Figure ∡𝑩𝑨𝑪 ∡ABC ∡BCA Result
(i)
(ii)
(iii)

11. The line joining from vertex of an isosceles triangle to join the
mid-point of the base is perpendicular to the base
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https://www.geogebra.org/m/Au4rzFcJ
https://www.geogebra.org/m/ErD5dhGt

12. The line joining from vertex of an isosceles triangle to join the mid-point of the
base is perpendicular to the base
• Three isosceles triangles ABC with different base BC are drawn
• Measuring the angles BMC and AMC in each triangles and tabulated
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EXPERIMENT - 4
Figure ∡𝑩𝑴𝑪 ∡AMC Result
(i)
(ii)
(iii)
M
M
M
Conclusion: The line joining from the vertex of an isosceles triangle to join the mid-point of base is
perpendicular to the base.

13. Base angles of an isosceles right angled triangle
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https://www.geogebra.org/m/ksRTgq9N

14. Base angles of an isosceles right angled triangle
• Three isosceles right angled triangles ABC at C of different sizes are drawn
• Measuring the ∡ABC and ∡CBA in each triangles and tabulated
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EXPERIMENT - 5
Figure ∡𝑨𝑩𝑪 ∡𝐂𝐁𝐀 Result
(i) ∡𝑨𝑩𝑪 = ∡𝐂𝐁𝐀 = 450
(ii)
(iii)
Conclusion: The base angles of an isosceles right angled triangle are always 450
Fig. (i)
Fig. (ii) Fig. (iii)

15. • ∡C = ∡B [ Base angles of an isosceles triangle]
= 550
• ∡A +∡B + ∡C = 1800 [sum of interior angles of triangle]
∡A + 550 + 550 = 1800
∡A = 1800 – 1100
• = 700
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1) Find unknown angles

16. • ∡N = 9 00 – 400[remaining angle of right
angled triangle]
• ∡N = 500
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2)

17. Find the unknown angles
X + 2x + x + 200 = 1800 [Sum of angles of triangle]
4x = 1800 -200
4x = 1600
X = 400
∡R = 400
∡Q = 2x = 2x400 = 800
∡P = x + 20 0 = 400 + 200 = 600
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3)

18. x0 + 600 + 300 = 1800 [sum of angles of triangle]
x0 + 900 = 1800
x0 = 1800 – 900
x = 900
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4)

19. • x = y = 450[ Base angles of an isosceles right angled
triangle
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5)

20. 6/27/2020 JANAK SINGH SAUD 20
• x = y [base angles of an isosceles triangle
x + y + 440 = 1800 [ sum of angles of triangle]
x + x + 440 = 1800 [ x = y]
2x = 1800 – 440
2x = 1360
x = 680
y = 680
Hence, x = y = 680
6)

21. x + 200 = 900 [sum of remaining angles of right angled
triangle]
x = 900 - 200
x = 700
y = x [ base angles of isosceles triangle]
x = y = 700
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7)

22. x + 1500 = 1800 [Liner pairs]
x = 1800 – 1500
= 300
x + y = 900 [ Acute angles of right angled triangle]
300 + y = 900
y = 900 – 300
y = 600
Hence, x = 300 and y = 600
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8)

23. x + 2x0 + 6x0 = 1800 [Sum of angles of triangles]
Or, 9x0 = 1800
Or, x = 200
Now, x = 200
2x = 2 x 200 = 400
6x = 6 x 200 = 1200
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9)

24. i) x = y [Base angles of an isosceles triangle]
ii) x + y = 1200 [Exterior angles of triangle]
or, x + x = 1200 [x = y]
or, 2x = 1200
or, x = 600
ii) z + x = 1800 [Linear pair]
or, z + 600 = 1800
or z = 1800 – 600
or, z = 1200
Hence, x = y = 600 and z = 1200
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10)

25. • x + 600 = 1800 [Linear pair]
x = 1800 – 600
x = 1200
• y + 450 = x0 [Exterior angle of a triangle]
or, y + 450 = 1200
or, y = 1200 – 450
or, y = 750
Hence , x = 1200 and y = 750
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11)

26. • y0 = 380 [Alternate angles]
• z0 = 420 [Alternate angles]
• x + z + 380 = 1800 [interior angles of a triangle]
or, x + 420 + 380 = 1800 [z = 420]
or, x + 800 = 1800
or, x = 1800 – 800
or, x = 1000
Hence, x = 1000, y = 380 and z = 420
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12)

27. • x = 600 [Corresponding angles with // lines]
• (y + 600) + 650 = 1800 [Co-interior angles with // lines]
or, y + 1250 = 1800
or, y = 1800 – 1250
or, y = 550
Hence, x = 600 and y = 550
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13)

28. 14) Find the value of x and y
• x + 2x + 450 = 1800 [Interior angles of a triangle]
or, 3x = 1800 – 450
or, 3x = 1350
or, x = 450
• y = 2x [Alternate angles with // lines]
or, y = 2 x 450
or, y = 900
Hence x = 450 and y = 900
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29. 6/27/2020 JANAK SINGH SAUD 29
15) In the figure ABCD is an equilateral triangle and BCD is an isosceles triangle
in which BC = CD. Find ∡CBA
i. ∡ABD = 600 [∆ABD is an equilateral
triangle]
ii. ∡CBD = ∡CDB [In ∆BCD, BC = CD]
iii. ∡CBD + ∡CDB + 1000 = 1800 [Sun of angles of a triangle]
∡CBD + ∡CBD + 1000 = 1800
2 ∡CBD = 1800 – 1000
2 ∡CBD = 800
∴ ∡CBD = 400
Lastly, ∡CBA = ∡ABD + ∡CBD [Whole part axiom]
= 400 + 600
= 1000

30. 6/27/2020 JANAK SINGH SAUD 30
15) If a base angle is double of the vertical angle of an isosceles triangle, then find
all the angles.
Let ABC is an isosceles triangle in which AB = AC and the vertical angle = ∡A = x
Then by the question ∡B = ∡C = 2x
Now, ∡A + ∡B + ∡C = 1800 [Sum of angles of triangle]
or, x + 2x + 2x = 1800
or, 5x = 1800
or,
5𝑥
5
=
1800
5
or, x = 360
Hence, the vertical angle = ∡A = x = 360
Each base angles = ∡B = ∡ C = 2x = 2(360) = 720
A
B C
x
2x 2x

31. https://www.youtube.com/channel/UCGxSYD_UZLzXfmAzxaRyYhw?vie
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6/23/2020 JANAK SINGH SAUD 31