Triangles

1. Triangles Sides and Angles

2. Triangles “We see triangles in our life on a daily basis such as the video that I am going to show you. This will play for the next minute and a half. It will show you what is done with the triangle instrument, especially in music. Please keep in mind what type of triangle you will see and write your guess in your notes. http://youtu.be/3rf2fU0bt0I

3. Angles and Triangles “As you’ve accessed the website, www.regentsprep.org and going to the ‘Geometry’ section, specifically the ‘Angles and Triangles’ portion, you can see that triangles are classified by sides. From the pictures that you see, these triangles are categorized into three parts: Scalene, isosceles, and equilateral.” http://www.regentsprep.org/Regents/math/geometry/GP5

4. Sides of Triangles • Accessing the www.regentsprep.org to go to the Geometry section, the sides of triangles. • Each triangle is classified by scalene, isosceles and equilateral. Can you think of what type of triangle that was used in the YouTube video about the triangle instrument? The triangle that was used was an equilateral triangle.

5. Scalene Triangles When you look at the scalene triangle. All the sides are different lengths or do not have congruent sides. How many remember what the word, congruence, means? Discuss within your group for a minute, please and then I’ll choose a group for an answer. (Ans: equal) Remember that term for the next slide.

6. Isosceles triangle Within the website, www.regentsprep.org, that we are continuing about our discussion about triangles. The next type of triangle is an isosceles which displays two congruent sides. Note the congruent symbols of the sides. Also, look at the triangle which is labeled as two legs and a base.” Please continue and click to view the isosceles triangle. http://www.regentsprep.org/Regents/math/geometry/GP5/

7. Equilateral triangle • From the website, www.regentsprep.org, we are looking at the sides of triangles. • Think about the next one: equilateral which also means ‘equal sides.’ This has three sides and again, look at the image which shows each side being equal to 10. • http://www.regentsprep.org/Regents/math/geometry/GP5/LTriangle.htm

8. Angles of triangles • At the website, www.regentsprep.org, discussing the angles of a triangle. • Here you have four types but this time, it is the ANGLES, not the sides. They are acute, right, obtuse, and equiangular triangles. Please note that all the insides add up to? Please discuss within your groups and I will call upon that group. (The answer is 180 degrees) • www.regentsprep.org/Regents/math/geometry/angles

9. Acute triangle • In viewing the website, regentsprep.org about triangles and its angles. Our focus is on: • Acute triangles are just that---cute. See how small their angles are? The triangle show all angles less than 90 and when added, it should be 180 degrees. • Acute triangle

10. Right triangle • At the website, regentsprep.org about triangles. • The right triangle has a small box or 90 degrees that shows you that it has a right angle. If you remember the Pythagorean Theoremfor right triangles, the longest side is called the hypotenuse, which is always opposite the right angle.” • Right triangle

11. Obtuse triangle • At the website,regentsprep.org: • The next type of triangle is an obtuse triangle---where one angle measures more than 90 degrees. So, where you see one “wide mouth’ of an angle of a triangle, you know it is an obtuse triangle.” • Obtuse triangle

12. Equiangular triangle • Equiangular triangle - regentsprep.org • Our last triangle—the equiangular triangle is where you have equal angles and it is like our equilateral triangle. This is a very unique triangle, especially for balance or for structure. • Equiangular triangle

13. Practice with triangles • Practice with triangles on the website, regentsprep.org • Let’s practice a few of these problems to review what we learned.

14. Practice #1 • Practice #1 - regentsprep.org • This asks what type of triangle will we get, based on the given angles? Talk amongst your groups to find an answer and give a reason. I will call upon the group I choose ‘randomly.’ • The answer is obtuse and if you click on the explanation, it will show you. • Practice #1

15. Practice #2 • Practice #2 – from regentsprep.org • This next problem is much like an Algebra equation so when you approach the ratios, ‘1: 3: 5,’ you would see it as adding 1x to 3x to 5x to be equal to the total amount of the insides of an angle. Which is how many degrees?” The answer would be 180 degrees. So, 1x+3x+5x= 180. Solve for x. • Click here for an answer with an explanation.

16. TICKET OUT THE DOOR • Practice #3 - regentsprep.org • This last one is your ticket out the door so please use the half sheets that I just handed out to you. Problem #3 says, “The vertex angle of an isosceles triangle measures eight times the measure of a base angle. Find the measure of a base angle.” Now how do we do this? It would help to first draw a picture but remember which is the base angle to the vertex angle? Next, write an equation and work within your groups. Show the explanation with the solution of x = 18. I will wait for a solution. Check the site for an explanation.

17. In closing • Hopefully by now you can view triangles through two aspects: sides and angles. As you begin your assignment, you will be able to solve for the sides or the angles based on what you have learned. Are there any questions? • If so, please visit me during Advisory or email me at dlynch@phoenixunion.org

18. References • Images from Microsoft and Google • Sound from Power Point • “Sides and Angles” – courtesy of regentsprep.org