Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Euler angles wikipedia , lookup
Golden ratio wikipedia , lookup
Apollonian network wikipedia , lookup
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Euclidean geometry wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Incircle and excircles of a triangle wikipedia , lookup
Triangle Angle Sum Theorem This theorem states that the sum of the angles in any triangle is 180⁰. This means that before any triangle can be form, we have to make sure their angles add up to be 180⁰. _________________________INDEPENDENPENT PRACTICE___________________ 1. Tom drew ∆NET, which is shown below. 3. Derek drew the following triangle: What is the name of this triangle? Based on the information in the triangle, what type is it? A. Acute Scalene triangle A. Right C. Scalene B. Acute D. Obtuse 4. Ciara constructs a triangle with angles measuring 65⁰ and 38⁰. What must be true of the measure of the third angle in her construction? B. Obtuse Isosceles triangle A. It must measure exactly 77⁰ C. Acute Isosceles triangle B. It must measure exactly 87⁰ C. It can have measure less than 103⁰ D. Right Triangle 2. Which of the following set of angle measures would make a triangle? A. 10⁰, 50⁰, 70⁰ C. 100⁰,60⁰,30⁰ B. 100⁰,50⁰,30⁰ D. 80⁰, 90⁰,20⁰ D. It can have any measure greater than 27⁰ 5.. Below is a yield sign: 7. When drawing the triangle PIN, Ericka wants to find the measure of the missing angle. If all the sides are congruent, what type triangle is it? A. 40⁰ A. Equilateral B. 60⁰ B. Scalene C. Obtuse D. Isosceles 6. One day, Mrs. Carter, Coach Lombard, Mr. Hill, and Mrs. Blackledge went for a trail walk for some exercise. The path they walked is shown below. C. 30⁰ D. 50⁰ 8. What statement is true about Isosceles triangles? A. They have two congruent sides only B. They have no sides congruent but all angles congruent C. They have congruent sides and congruent angles D. They have two congruent sides and two congruent angles Their route resembles a A. Right Triangle B. Obtuse Triangle C. Straight Triangle D. Acute Triangle Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. x+y>z x+z>y y+z>x COACHED EXAMPLE Is it possible to construct a triangle with sides measuring 8 feet, 9 feet, and 12 feet? The triangle inequality theorem states that sum of the lengths of any two sides of a triangle must be________________________ than the length of the third side. Use the theorem to determine if this triangle is possible or not. Is 8 + 9 > 12?______________________________ Is 8 + 12 > 9?______________________________ Is 9 + 12 > 8?______________________________ The inequalities above are all true, so it____________possible to draw a triangle with side lengths of 8 feet, 9 feet, and 12 feet. Lets explore these for ourselves by completing some practice. For questions 1-6, tell whether a triangle can be constructed using the give measure 1. 2 in, 2 in, 3 in 4. 8 in, 7 in, 15 in 2. 3 ft, 15 ft, 9ft 5. Lincoln constructs a triangle with one side 5 inches long and another side 7 inches long. Which is not a possible length for the third side? A. 3 inches B. 6 inches C. 11 inches D. 12 inches 3. 4 yd, 6 yd, 5 yd 6. Maggie constructs a triangle with one side 7 centimeters long and another side 10 centimeters long. Which is not a possible length for the third side? A. 2 centimeters B. 4 centimeters C. 7 centimeters D. 16 centimeters