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Geometry Notes Section 4-1

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What you’ll 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 vertices of this triangle are:**

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 The vertices of this triangle are: F, S, and H

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**The sides of this triangle are:**

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

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**The angles of this triangle are:**

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 The angles of this triangle are: F S H F or SFH, S or FSH, and H or SHF

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**You must include the Δ symbol**

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

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**Classifying Triangles by Angles**

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

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**Classifying Triangles by Sides**

Scalene Triangles—triangles with no 3 sides of equal measure (no congruent sides) Isosceles triangles—triangles with at least TWO sides of equal measure (2 congruent sides) Equilateral Triangles—triangle with all sides exactly the same measure (all 3 sides congruent to each other)

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**Parts of an Isosceles Triangle**

Vertex angle Vertex angle Vertex angle The vertex angle is always the angle between the two congruent sides; the other angles are called base angles.

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

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

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

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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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