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Geometry A Unit 4 Day 1 4.1 Triangles and Angles I. Warm-Up / Introduction A. Vocabulary WORD BANK Acute Triangle Isosceles Triangle . Equiangular Triangle Scalene Triangle Equilateral Triangle Obtuse Triangle, Right Triangle Fill in the blank with the word from the WORD BANK that matches the definition. 1. _______________________ - A triangle with 2 or more equal sides. 2. _______________________ - A triangle with 3 equal sides. 3. _______________________ - A triangle with no equal sides. 4. ___________________ - A triangle with one 90 angle. 5. ___________________ - A triangle with one angle measuring more than 90 . 6. ___________________ - A triangle with all angles measuring less than 90 . 7. ___________________ - A triangle that has three angles with the same measure. One thing to be aware of, every EQUILATERAL TRIANGLE is an ISOSCELES TRIANGLE… Explain: _____________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ …but not every ISOSCELES TRIANGLE is an EQUILATERAL TRIANGLE It’s just that calling an equilateral triangle an isosceles one is not being as specific as possible. B. Proof of a Property You Probably Knew 4 1 5 Given: AB | | CD Prove: 1 + 2 + 3 = 180o. Statement Reason 2 1. ________________________ 1. ____________________ 180 2. ________________________ 2. Linear Trio/Definition of Straight Angle 3. _________________________ 3. ___________________ 4. ________________________ 4. ___________________ 5. ________________________ 5. _____________________ The very useful result of the proof above is the “Triangle Sum” Theorem (Interior) Triangle Sum – The three (interior) angles of any triangle add to 180o. This sets up a second thing to be aware of. Every EQUIANGULAR TRIANGLE is an ACUTE TRIANGLE… Explain: _____________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ …but not every ACUTE TRIANGLE is an EQUIANGULAR TRIANGLE It’s just that calling an equiangular triangle an acute one is not being as specific as possible. 3 Applications of Definitions and Theorem Problem Set #1. Classify each of the following. Use at least one word from each list. List A: Equilateral, Isosceles and Scalene Ex. 1: List B: Acute, Obtuse, Right and Equiangular Ex. 2: 59 30 ________________________ and _________________________ and _______________________ _________________________ 60 Ex. 3: 60 ________________________ and _______________________ Ex. 4: Find x and determine if ABC is right acute or obtuse and whether it is scalene equilateral or isosceles. A = 3x 40 B = x C = 3x 10 ____________________________ ____________________________ C. A Second Round of Vocabulary N Below, the definitions of Legs and Hypotenuse are given. Name the legs and the hypotenuse in the right triangle drawn. L M 1. Leg – A side of a right that helps form the right . ______ and _______ 2. Hypotenuse – The side of the right across from the right . _________ D D. Parts of and Isosceles Triangle Below, the definitions of Base, Base Angle, Legs and Vertex Angle are given. Name each in the isosceles triangles drawn. 1. Leg - One of the sides of equal length. ______ and ______ 2. Base - The side that connects the legs. ________ E F E 3. Vertex Angle - The angle included between the legs of an isosceles triangle. ____________ D 4. Base Angle - One of the angles included between the base and one of the legs. _____ and ______ One thing to consider about the two different meanings of the word “legs”. In an isosceles right triangle, is there any concern that the legs (two sides that make the right angle) would not be the legs (the two sides that are equal). YES or NO ? Explain. _________________________________________________ _______________________________________________________________________ _______________________________________________________________________ F