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Geometry

Geometry . Notes Section 4-1. 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. Vocabulary. Sides of a triangle Vertices of a triangle Acute triangle Obtuse triangle

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Geometry

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  1. Geometry Notes Section 4-1

  2. 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.

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

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

  5. S F H 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: FS, SH, and HF

  6. S F H 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 orSFH, S orFSH, and H orSHF

  7. 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

  8. 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)

  9. 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)

  10. 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.

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

  12. 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 G x + 5 3x – 9 F H 2x - 2

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

  14. 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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