Properties of Proportions
I.SectionObjectives
- Prove theorems about proportions.
- Recognize true proportions.
- Use proportions theorem in problem solving.
II.MultipleIntelligences
- This is a brief lesson used to explain the corollary theorems associated with the Cross Multiplication Theorem.
- To make this lesson more interesting and interactive, use group work.
- Divide the students into five groups.
- After teaching the lesson and going through the material, assign each group one of the corollary theorems.
- Then put an example of two similar triangles (with measurements) on the board/overhead.
- Ask each group to use the example on the board to create an example that illustrates their corollary theorem.
- Allow time for the students to work and then have each group present their example to the class.
- When finished, encourage the other students to ask questions to see how well the students in the group can
answer them. - Answering questions is a great way to assess student understanding.
- Intelligences- linguistic, logical- mathematical, visual- spatial, interpersonal, intrapersonal.
III.SpecialNeeds/Modifications
- Write these notes on the board/overhead. Request that students copy them down.
- Cross Multiplication Theorem- defining property of proportions.
- Subtheorems are called corollary theorems.
- Review which terms in a proportion are the means and the extremes.
- Corollary 1- swap means.
- Corollary 2- swap extremes.
- Corollary 3- flip it upside down.
- Corollary 4−a+bb=c+dd
- Corollary 5−a−bb=c−dd
IV.AlternativeAssessment
- Assessment can be done through student questions and answers following the exercise.
Similar Polygons
I.SectionObjectives
- Recognize similar polygons.
- Identify corresponding angles and sides of similar polygons from a statement of similarity.
- Calculate and apply scale factors.
II.MultipleIntelligences
4.7. Similarity