# Chapter 5: Basic Geometry TE - Problem Solving

**Problem Solving in Geometry**

Problem solving and applications are particularly challenging for many students. Let the students know that this is difficult for most people and that with time they will get better at it. They are probably going to struggle, have to reread the information several times, and may be confused for a while. It is all part of the process. This section will give them strategies to work through the difficulties without giving up.

**Highlight Important Information** - It is nice when students can actually mark up the text of the exercise, but frequently this is not the case. As they read the paragraph have the students take notes or organize the information into a chart or diagram. Otherwise the students can just get lost in all the words. Translating from English to math is often the hardest part.

**The Last Sentence** - When the students are faced with a sizable paragraph of information the most important sentence, the one that asks the question, is usually at the end. Advise the students to read the last sentence first, then as they read the rest of the paragraph they will see how the information they are being given is important.

**Does This Make Sense?** - It is so hard to get the students to ask themselves this question at the end of a word problem or application. I think they are so happy to have an answer they do not want to know if it is wrong. As you examples in class, model the process of checking the validity of the answer. Give examples of obviously wrong answers-like a hypotenuse that turns out to be shorter than a leg in a right triangle or angles in a triangle that don’t add up to 180 degrees. Many students really don’t know how to determine whether their answer is reasonable. Keep reminding them and giving examples. Sometimes it is possible to not accept work with an obviously wrong answer. The paper can be returned to the student so they can look for their mistake. This is a good argument for the importance of showing clear, organized work.

**Naming Quadrilaterals** - When naming a quadrilateral the letter representing the vertices will be listed in a clockwise or counterclockwise rotation starting from any vertex. Students are accustomed to reading from left to right and will sometimes continue this pattern when naming a quadrilateral.

**The Pythagorean Theorem** - Most students have learned to use the Pythagorean Theorem before Geometry class and will want to use it instead of the distance formula. They are closely related; the distance formula is derived from the Pythagorean Theorem as will be explained in another chapter. If they are allowed to use the Pythagorean Theorem remind them that it can only be used for right triangles, and that the length of the longest side of the right triangle, the hypotenuse, must be substituted into the variable if it is known. If the hypotenuse is the side of the triangle being found, the stays a variable, and the other two side lengths are substituted for and .

## Chapter Outline

- 5.1. Basics of Geometry
- 5.2. Reasoning and Proof
- 5.3. Parallel and Perpendicular Lines
- 5.4. Triangles and Congruence
- 5.5. Relationships with Triangles
- 5.6. Polygons and Quadrilaterals
- 5.7. Similarity
- 5.8. Right Triangle Trigonometry
- 5.9. Circles
- 5.10. Perimeter and Area
- 5.11. Surface Area and Volume
- 5.12. Rigid Transformations