Angles

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Teaching Outlines

Concept #1.What is an angle ?

Activities

Foramtion of

Concept #2. Using a Protractor- Measuring an angle

Learning objectives

Notes for teachers

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Concept #3.Types of angles

Learning objectives

Notes for teachers

Activity No #1.Crazy Angles using Geogebra

  • Estimated Time: 40 minutes
  • Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
  • Prerequisites/Instructions, if any:
  1. The students should have a basic understanding about point, rays, line segments and vertex.
  2. They should know how angles are formed.
  3. They should know that angles are measured in units called degrees. 360 ° is a full rotation (a circle)
  4. They should know to use a protractor and measure the angles.
  5. They should know the meaning of terms acute, obtuse, straight, reflex, and complete angles.
  • Multimedia resources; Laptop
  • Website interactives/ links/ / Geogebra Applets

  • Process:
  1. The teacher should recaptulate the concept of a point, line segment, ray, vertex and angles.
  2. The teacher should show how angles are formed.
  3. Discuss the concept of cartesian plane, X and Y axes, rotation, and how it relates to angles.
  4. Demonstrate how to measure angles using a protractor.
  5. Define and illustrate the classification of the types of angles—acute, obtuse, right, straight zero and complete angles.
  6. In the succeeding class give the students protractors and let them have enough practise measuring and classifying angles.

Developmental Questions:

  1. What is a point ?
  2. A minimum of how many points are needed to define a line segment ?
  3. A minimum of how many points are needed to form an angle ?
  4. Name the line segments from the figure.
  5. What is a vertex ?
  6. How many rays /line segments are needed to form an angle ?
  7. Name the vertex at which the angle is formed
  8. Name the angle .
  9. Name the type of angle formed.
  • Evaluation:
  1. Assess the students knowledge of angles by projecting different types of angles and asking them to name
  2. What are the characteristics of an acute angle ?
  3. What are the characteristics of an obtuse angle?
  4. What are the characteristics of a right angle
  5. Evaluate if the students have understood that :
  • An angle is formed where 2 lines meet at a point.
  • A right angle looks like a corner of a square or a rectangle.
  • An acute angle is narrower than a right angle.
  • An obtuse angle is wider than a right angle.
  • Question Corner:
  1. What is an angle ?
  2. Where do you name an angle ?
  3. How do you identify different types of angles in 2-dimensional figures?
  4. How do angles help to classify 2-dimensional figures?
  5. Are angles <ABA' and <A'BA the same ? Justify
  6. Differentiate between the zero angle and a complete angle.

Concept # 4. Angle constructions

Learning objectives

Notes for teachers

Activity No #

Concept # 5. Angle bisector-Its construction

Learning objectives

Notes for teachers

Activity - Construction of angle with measure 22.5∘

This activity helps to illustrate the 'angle bisector' construction three times since we construct ∡22.5 by constructing ∡90∘ (bisecting a segment / straight angle ∡180∘, then bisect ∡90∘ to get ∡45∘ and finally bisect ∡45∘ to get ∡22.5∘).

Concept # 6. Pairs of angles

Learning objectives

Notes for teachers

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Concept # 7.Angles formed when lines are cut by a transversal

Learning objectives

Notes for teachers

Activity No # 1.Angles formed when a transversal intersects parallel lines

*Estimated Time : 40 minutes
*Materials/ Resources needed :Laptop, geogebra file, projector and pointer.
*Prerequisites/Instructions, if any :

  1. The students should have prior knowledge of parallel lines , transversal, angles and types of angles formed when a pair of parallel lines are intersected by a transversal.
  2. They should know what the terms interior, exterior, adjacent, alternate, consecutive, congruent, linear and corresponding mean.
  3. Students should know the definition of complementary angles, supplementary angles, and congruent angles.

*Multimedia resources: Laptop
*Website interactives/ links/ / Geogebra Applets

  • This is a resource file on 'vertically opposite angles'


It has been created by Sucheta, Mathematics teacher, GHS Thyamangondlu

*Process:

  1. Reiterate that when a transversal intersects parallel lines, several pairs of congruent and supplementary angles are formed.
  2. Have students draw two parallel lines and a third line(transversal) intersecting those two lines on their own paper. Direct them to think about any angle relationships they see. Have them discuss their conjectures with a partner.
  3. The teacher can next project the GeoGebra worksheet and discuss about types of angles and their relationships with the class .
  4. Finally the teacher and students can summarize together the angle relationshipsalong with their characteristics.

Linear pair of angles - adjacent and supplementary

  • Vertical angles - congruent
  • Corresponding angles -congruent
  • Alternate interior angles - congruent
  • Same side interior angles - supplementary
  • Alternate exterior angles - congruent
  • Same side exterior angles - supplementary

*Developmental Questions :(What discussion questions)

  1. How many pairs of corresponding angles are there ?
  2. What is true about corresponding angles formed when parallel lines are cut by a transversal?
  3. Compare different pairs of alternate interior angles. What do you notice?
  4. <EGD and <AHF are alternate exterior angles. What is another pair of alternate exterior angles?
  5. Compare different pairs of same-side interior angles. What do you notice?
  6. Compare different pairs of same-side exterior angles. What do you notice?

*Evaluation:

  1. What are the characteristics of linear angles (adjacent and supplementary) ?
  2. What do you observe about the angle measures of the linear angles?

*Question Corner:

  1. What do adjacent , alternate, linear , corresponding and consecutive mean individually
  2. What are complementary angles?
  3. What are supplementary angles ?
  4. What does it mean if two angles are congruent?
  5. What is the complement of 65 degrees
  6. What is the supplement of 70 degrees?
  7. Compare angle relationships formed by parallel lines vs. angle relationships formed by non-parallel lines.

Activity No 2 Angles formed when a transversal intersects parallel lines

  • Estimated Time : 90 minutes
  • Materials/ Resources needed

Laptop, geogebra file, projector and pointer.

  • Prerequisites/Instructions, if any
  1. The students should have prior knowledge of parallel lines , transversal, angles and types of angles formed when a pair of parallel lines are intersected by a transversal.
  2. They should know what the terms interior, exterior, adjacent, alternate, consecutive, congruent, linear and corresponding mean.
  3. Students should know the definition of complementary angles, supplementary angles, and congruent angles.
  • Multimedia resources:

Laptop

  • Website interactives/ links/ / Geogebra Applets

111.png

  • Process
  1. Reiterate that when a transversal intersects parallel lines, several pairs of congruent and supplementary angles are formed.
  2. Have students draw two parallel lines and a third line(transversal) intersecting those two lines on their own paper. Direct them to think about any angle relationships they see. Have them discuss their conjectures with a partner.
  3. The teacher can next project the GeoGebra worksheet and discuss about types of angles and their relationships with the class .
  4. Finally the teacher and students can summarize together the angle relationships.

Linear pair of angles - adjacent and supplementary
Vertical angles - congruent
Corresponding angles -congruent
Alternate interior angles - congruent
Same side interior angles - supplementary
Alternate exterior angles - congruent
Same side exterior angles - supplementary

  • Developmental Questions
  1. How many pairs of corresponding angles are there ?
  2. What is true about corresponding angles formed when parallel lines are cut by a transversal?
  3. Compare different pairs of alternate interior angles. What do you notice?
  4. <EGD and <AHF are alternate exterior angles. What is another pair of alternate exterior angles?
  5. Compare different pairs of same-side interior angles. What do you notice?
  6. Compare different pairs of same-side exterior angles. What do you notice?

Evaluation

  1. What are the characteristics of linear angles (adjacent and supplementary) ?
  2. What do you observe about the angle measures of the linear angles?
  • Question Corner
  1. What do adjacent , alternate, linear , corresponding and consecutive mean individually
  2. What are complementary angles?
  3. What are supplementary angles ?
  4. What does it mean if two angles are congruent?
  5. What is the complement of 65 degrees
  6. What is the supplement of 70 degrees?
  7. Compare angle relationships formed by parallel lines vs. angle relationships formed by non-parallel lines.

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