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Geometry Notes Section 4-1

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What youll learn.... How to identify and name the parts of a triangle. How to identify and classify triangles by angles. How to identify and classify triangles by sides.

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Vocabulary Sides of a triangle Vertices of a triangle Acute triangle Obtuse triangle Right triangle Equiangular triangle Scalene triangle Isosceles triangle Equilateral triangle

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The parts of a triangle The vertices of a triangle are the corner points joining the sides of the triangle Points are named with capital printed letters One corner is called a VERTEX more than one, VERTICES F S H F,S,and H The vertices of this triangle are:

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The parts of a triangle The sides are line segments Segments are named by endpoints Sides will have measure (like inches) F S H FS,SH,and HF The sides of this triangle are:

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The parts of a triangle Every triangle will have three angles Angles are named by with three points (vertex in middle), with just the vertex, or with a number F S H F or SFH, The angles of this triangle are: S or FSH, and H or SHF

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NAMING A TRIANGLE Triangles are named by their vertices A C T THIS TRIANGLE CAN BE CALLED ΔACT ΔTAC ΔCAT You must include the Δ symbol

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Classifying Triangles by Angles Acute Acute Trianglestriangles with all 3 angles measuring less than 90° Obtuse trianglestriangles with exactly ONE angle measuring between 90° and 180° Right Triangles– triangles with exactly ONE right angle (marked with a box) Equiangular Trianglestriangle with all angles exactly the same measure (all are congruent to each other)

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Classifying Triangles by Sides Scalene Trianglestriangles with no 3 sides of equal measure (no congruent sides) Isosceles trianglestriangles with at least TWO sides of equal measure (2 congruent sides) Equilateral Trianglestriangle with all sides exactly the same measure (all 3 sides congruent to each other)

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Parts of an Isosceles Triangle vertex base The vertex angle is always the angle between the two congruent sides; the other angles are called base angles. Vertex angle Vertex angle

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Example Problem #1: Find x if ΔJMN is isosceles with JM = MN. 3x – 9 x - 2 2x – 5 M NJ

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Example Problem #2: ΔFGH is equilateral. With FG = x + 5, GH = 3x – 9, and FH = 2x - 2. Find x and the length of each side 3x – 9 2x - 2 x + 5 G HF

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Example Problem #3: Classify ΔRST by its sides. S(2, 5)T(4, 2)R(0, 2) S TR

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Have you learned.... How to identify and name the parts of a triangle? How to identify and classify triangles by angles? How to identify and classify triangles by sides? Assignment: NON-PROOF:Worksheet 4-1 PROOF: P. 181(22-44E, 50-56E)

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