Difference between revisions of "Activity-construction of angles"
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===Process (How to do the activity)=== | ===Process (How to do the activity)=== | ||
| − | # | + | # Ask students which angle could be drawn with a scale? (Straight Angle) |
| + | # If we can 'halve' any angle, then we can derive angles from the straight angle - in succession, this would be as follows - ∡180∘ -> ∡90∘, ∡90∘ -> ∡45∘, ∡45∘ - > ∡22.5∘ and so on. | ||
| + | # Explain the process of constructing an Angle bisector using only compass (without using a protractor). Students can follow and do the construction in their books | ||
| + | ## Draw a line segment or a line. Identify a point on this segment. We can treat this point as the vertex of a straight angle | ||
| + | ## Construct two arcs from the vertex of the straight angle, such that each cuts the line segment on either side of the vertex. | ||
| + | ## Plot the intersection point of each arc and the arms of the straight angle. | ||
| + | ## From each intersection, draw an arc of same measure, such that the two arcs intersect. | ||
| + | ## Plot the intersection point of these two arcs | ||
| + | ## Construct a line segment (or line or ray) from the vertex to this intersection point. | ||
| + | ## This process will create two angles. Measure both angles. They will be 90 each | ||
| + | ## Why does this process work? (Explanation - locus of points equidistant from the two points which are equidistant from the vertex) | ||
| + | ## Following the same process. construct the bisector of one of these two right angles. We will get two angles of 45 each | ||
| + | ## Following the same process. construct the bisector of one of these angles, which measure 45. We will get two angles of 22.5 each | ||
| + | # You can use the 'Play - Construction protocol' to show the above steps one by one. But do this after constructing the bisectors using Geogebra. | ||
===Evaluation at the end of the activity=== | ===Evaluation at the end of the activity=== | ||
| − | + | # Ask students, what are the other angles that can drawn in the same construction. (Hint, there are new angles created, which are adjacent/ complementary / supplementary to the angles we have discussed. For eg. we get an angle with measure 135 (by considering one 90 and one 45 angles adjacent to each other). | |
[[Category:Lines and Angles]] | [[Category:Lines and Angles]] | ||
[[Category:Class 9]] | [[Category:Class 9]] | ||
Revision as of 05:40, 2 November 2019
Construction of an angle with measure 22.5∘
Objectives
Understand construction of an angle bisector,
Problem Class 9. Construction of an angle with measure 22.5∘
Estimated Time
One period
Prerequisites/Instructions, prior preparations, if any
Introduction to Angles
Materials/ Resources needed
Geogebra file Construction of angle with measure 22.5∘
Process (How to do the activity)
- Ask students which angle could be drawn with a scale? (Straight Angle)
- If we can 'halve' any angle, then we can derive angles from the straight angle - in succession, this would be as follows - ∡180∘ -> ∡90∘, ∡90∘ -> ∡45∘, ∡45∘ - > ∡22.5∘ and so on.
- Explain the process of constructing an Angle bisector using only compass (without using a protractor). Students can follow and do the construction in their books
- Draw a line segment or a line. Identify a point on this segment. We can treat this point as the vertex of a straight angle
- Construct two arcs from the vertex of the straight angle, such that each cuts the line segment on either side of the vertex.
- Plot the intersection point of each arc and the arms of the straight angle.
- From each intersection, draw an arc of same measure, such that the two arcs intersect.
- Plot the intersection point of these two arcs
- Construct a line segment (or line or ray) from the vertex to this intersection point.
- This process will create two angles. Measure both angles. They will be 90 each
- Why does this process work? (Explanation - locus of points equidistant from the two points which are equidistant from the vertex)
- Following the same process. construct the bisector of one of these two right angles. We will get two angles of 45 each
- Following the same process. construct the bisector of one of these angles, which measure 45. We will get two angles of 22.5 each
- You can use the 'Play - Construction protocol' to show the above steps one by one. But do this after constructing the bisectors using Geogebra.
Evaluation at the end of the activity
- Ask students, what are the other angles that can drawn in the same construction. (Hint, there are new angles created, which are adjacent/ complementary / supplementary to the angles we have discussed. For eg. we get an angle with measure 135 (by considering one 90 and one 45 angles adjacent to each other).