Beige White Orange Simple All About Triangles Presentation - Copy.pptx

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1. Complete the table below. Interior angle 1 Interior angle 2 Exterior angle 34 36   54 78   64 56   24 45   55 27  

2. Illustrating Exterior Angle Inequality Theorem

3. FIND THE MISSING ONE 43 23 ? 43+23=66

4. 79 48 ? FIND THE MISSING ONE ?

5. m∠4+m∠3=180 m∠4=m∠1+m∠2 Formula:

6. Example m∠1=48 m∠2=? m∠3=79 m∠4=? 48 ? 79 ? Let’s place the value to the formula m∠4+79=180 m∠4=180-79 m∠4=180-79 m∠4=101 Now we know the m∠4 we can find now the value of m∠2 m∠4=m∠1+m∠2 101=48+m∠2 101-48=m∠2 53=m∠2 So m∠4=101 and m∠2=53

7. You're designing a fantastical mural for the school cafeteria. Part of the design includes a giant, friendly monster with three horns! We know two horn angles: Angle 1 is 45 degrees Angle 3 is a surprising 67 degrees Mystery Angle: The space between the two horns is also an angle, but you accidentally smudged the paint there! We can call this missing angle #2. Let’s have some another example

8. m∠1=45 m∠2=? m∠3=67 m∠4=? 45 ? 67 ? We must find first the m∠4 m∠4+67=180 m∠4=180-67 m∠4=113 Now we know the m∠4 we can find now the value of m∠2 m∠4=m∠1+m∠2 113=45+m∠2 113-45=m∠2 68=m∠2 So m∠4=113 and m∠2=68

9. Problem at the Farm: Missing Angle Mystery Mr. Santos is teaching his agriculture class about building sturdy fences at San Isidro Agricultural School. He wants to demonstrate how angles affect fence stability. Imagine a triangular fence post with a horizontal top bar and two diagonal supports. We know the angle (∠1) between the top bar and one support is 33 degrees because it's important for water to run off easily. We also know the angle (∠3) at the bottom between the two supports is 77 degrees for proper weight distribution. The problem is, you forgot to measure the angle (∠2) formed where one support meets the top bar (the remote interior angle to the exterior angle). Another example

10. m∠1=33 m∠2=? m∠3=77 m∠4=? 33 ? 77 ? We must find first the m∠4 m∠4+77=180 m∠4=180-77 m∠4=103 Now we know the m∠4 we can find now the value of m∠2 m∠4=m∠1+m∠2 103=33+m∠2 103-33=m∠2 70=m∠2 So m∠4=103 and m∠2=70

11. Let's Practice!

12. Problem: You are exploring the historic walled city of Intramuros, Philippines. While navigating the narrow streets, you come across a charming triangular plaza with a bustling market on one side (∠1 = 55°) and a beautiful old church on another (∠3 = 80°). Unfortunately, you forgot to measure the angle formed by the street you came from and the market (∠2). You also wonder how wide the street appears compared to the market (∠4 Practice Exercise!!!

13. In this lesson I learned that ________________________

14. ILLUSTRATING THE EXTERIOR ANGLE INEQUALITY THEOREM PROVIDES A VALUABLE FOUNDATION FOR UNDERSTANDING TRIANGLE GEOMETRY, FOSTERING PROBLEM-SOLVING SKILLS, AND STRENGTHENING SPATIAL REASONING IN STUDENTS. VALUE

15. Assignment: Math Art Mystery! Ms. Lee is showing her 8th graders at Central Middle School how to create beautiful tessellations using triangles. But there's a mystery! Imagine you have a triangle with one right angle (∠3 = 90°). You also know that one of the other interior angles (∠1) measures 40 degrees. There's a missing angle (∠2) and an exterior angle (∠4) you haven't drawn yet. Challenge: Based on the triangle properties, what is the relationship between the missing angle (∠2) and the right angle (∠3)? Write this as an equation. Knowing the right angle and using the Exterior Angle Inequality Theorem, what can you say about the missing angle (∠2) compared to the exterior angle (∠4)? ASSIGNMENT !!!

16. Scalene Triangle A scalene triangle has no equal sides. All the sides are different lengths.

17. Which triangle is scalene?

18. Which triangle is isosceles?