5.2 What is the Side Relationship With the Angle? Pg. 5 Side Relationships.

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Presentation transcript:

5.2 What is the Side Relationship With the Angle? Pg. 5 Side Relationships

5.2 – What is the Side Relationship With the Angle? Side Relationships Now that you know when 3 lengths can form a triangle, you are going to examine the relationship between the sides and angles in any triangle. Then you are going to further your knowledge of right triangles and the Pythagorean theorem.

5.9 – TRIANGLE LENGTHS a. Examine at the triangle below. Measure the side lengths with a ruler and write it on the triangle. Then list the side lengths from smallest to largest. Then list the angles from smallest to largest.

2cm 5cm 6.8cm 25° 10°145° Sides: _______________________ Angles: ________________________

b. What is the relationship between the largest side and the largest angle? What about the smallest side and the smallest angle? 2cm 5cm 6.8cm 25° 10°145°

b. What is the relationship between the largest side and the largest angle? What about the smallest side and the smallest angle? 2cm 5cm 6.8cm 25° 10°145° They are opposite from each other

c. Imagine that became smaller. Which side length would change? 2cm 5cm 6.8cm 25° 10°145°

d. Imagine that became larger. Which side length would change? 2cm 5cm 6.8cm 25° 10°145°

e. What is always the longest side in a right triangle? 2cm 5cm 6.8cm 25° 10°145°

5.10 – ORDERING UP List the sides and angles in order from smallest to largest. Find the missing angles to help you.

Sides: ________________ Angles: _______________

Sides: _________________ Angles: ________________

<A = <C,<B 45°

<C,<C, <B,<A 60°

5.11 – WHAT'S THE PATTERN? Use the tools you have developed to find the lengths of the missing sides of the triangles below. If you know a shortcut, share it with your team. Look for any patterns in the triangles as you solve. Are any triangles similar and multiples of others? Keep answers in exact form.

5.12 – PYTHAGOREAN TRIPLES Karl noticed some patterns as he was finding the sides of the triangles above. He recognized that the triangles sides are all whole numbers. He also noticed that knowing the triangle in part (a) can help find the hypotenuse in parts (b) and (c). a. Groups of numbers like 3, 4, 5 and 5, 12, 13 are called Pythagorean Triples. Why do you think they are called that? Whole #s that make Pyth. thm true

b. What other sets of numbers are also Pythagorean Triples? How many different sets can you find? 3, 4, 5 6, 8, 10 9, 12, 15 12, 16, 20 5, 12, 13 10, 24, 26 15, 36, 39 20, 48, 52

5.13 – EXTRA PRACTICE Find the area of the shapes using Pythagorean triples to help find the missing sides.

8 3 4

8

A = 100un 2