Activity 13
OBJECTIVE
To
verify experimentally that if two lines intersect, then
Two transparent strips marked as AB and CD, a full protractor, a nail, cardboard, white paper, etc.
METHOD OF CONSTRUCTION
1. Take a cardboard of a convenient size and paste a white paper on it.
2. Paste a full protractor (0° to 360º) on the cardboard, as shown in Fig. 1.
3. Mark the centre of the protractor as O.
4. Make a hole in the middle of each transparent strip containing two intersecting lines.
5. Now fix both the strips at O by putting a nail as shown in Fig. 1.
DEMONSTRATION
1.
Observe the adjacent angles and the
vertically opposite angles formed in different positions of the strips.
2. Compare vertically opposite angles formed by the two lines in the strips in different positions.
3. Check the relationship between the vertically opposite angles.
4. Check that the vertically opposite angles ∠AOD, ∠COB, ∠COA and ∠BOD are equal.
5. Compare the pairs of adjacent angles and check that ∠COA + ∠DOA= 180º, etc.
6. Find the sum of all the four angles formed at the point O and see that the sum is equal to 360º.
OBSERVATION
On actual measurement of angles in one position of the strips :
|
1. |
∠AOD = ................. |
, ∠AOC =
................... |
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|
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∠COB =
................. |
, ∠BOD =
................. |
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|
|
Therefore, ∠AOD = ∠COB and ∠AOC =
............ |
(vertically opposite angles). |
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2. |
∠AOC + ∠AOD = ............. |
, ∠AOC + ∠BOC = |
..................., |
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|
|
∠COB + ∠BOD =
................... |
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|
|
|
|
∠AOD + ∠BOD = ................... |
(Linear pairs). |
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3. |
∠AOD + ∠AOC + ∠COB + ∠BOD = .................... |
(angles
formed at a point). |
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APPLICATION
These properties are used in solving many geometrical problems.
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