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Introductory Geometry: Congruence and Similarity

Coursework Instructions:

Please answer each of the following questions with 5 or more sentences. Use the textbook to help answer each question "A Problem Solving Approach to Mathematics for Elementary School Teachers". Read chapter 11 and 12 from A Problem Solving Approach to Mathematics for Elementary School Teachers.



1. Compare and contrast the English system and the metric system of linear measure. What is the origin of each? Are there advantages or disadvantages to either system? If you had a choice, which system would you teach your class as a primary system of measurement?



2. Explain the difference between interior and exterior angles of a polygon. Identify two theorems related to angles of a polygon and give an example of an application of each.



3. Explain in your own words the purpose and value of geometric constructions. What important lessons are to be learned through constructions? How can the concept of congruence be learned by doing a construction?



4. Define similar triangles and similar figures. Compare and contrast the various theorems which relate to the similarity of triangles. How would you teach these theorems to a class? Give examples.

Coursework Sample Content Preview:

Introductory Geometry: Congruence and similarity With Construction
Your Name
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Professor's Name
June 17, 2021
1 The English and metric systems are comparable in that they are both widely utilized as measuring systems today. The English System would require a conversion ratio (or unit variable) to shift between measures, whereas the Metric System merely changes the punctuation mark.
The British Weights and Measures Act of 1824, which specified the Imperial Units that will be used across the British Empire, started to standardize measurement in the English System.
On the other hand, the Metric System is claimed to have originated in France, when the government requested an unchanging measurement system dependent on the Earth's diameter.
Because the Metric System is always decimal, it is simpler to utilize in formulas but harder to explain. However, in conversation, the English method is considerably easier to explain but harder to use in formulas.
Because the Metric System is more exact than the English System, I believe it is better to use it when teaching measuring.
2 Exterior angles are calculated by measuring the distance from one side of the polygon to an extended exterior line. Inside the polygon, interior angles are measured from one side to the next.
Exterior Angle Theorem and the Exterior Sum Theorem
In the Exterior Sum Theorem, the total of the external angle measurements, one for each vertex, should be 360° if the polygon is convex.
For this example, the sum of the measures of the exterior angles of this polygon is 360o.
The External Angle Theorem states that the exterior angle of a triangl...
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