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Geometry

Geometry. Lesson 4 – 1 Classifying Triangles. Objective: Identify and classify triangles by angle measures. Identify and classify triangles by side measures. Classifications of Triangles by Angles. Acute Triangle 3 acute angles. Right Triangle 1 right angle. Obtuse Triangle

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Geometry

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  1. Geometry Lesson 4 – 1 Classifying Triangles Objective: Identify and classify triangles by angle measures. Identify and classify triangles by side measures.

  2. Classifications of Triangles by Angles Acute Triangle 3 acute angles Right Triangle 1 right angle Obtuse Triangle 1 obtuse angle Equiangular Triangle 3 congruent acute angles

  3. Classify each triangle as acute, equiangular, obtuse, or right. Acute Right Obtuse Equiangular

  4. Example Classify triangle PQR as acute, equiangular, obtuse, or right. Explain your reasoning. 104 Triangle PQR is obtuse since it has 1 obtuse angle Of 104 degrees.

  5. Your Turn Use the diagram to classify triangle PQS as acute, equiangular, obtuse, or right. 90 Triangle PQS is a right triangle since it has a right angle.

  6. Classifying Triangles by Sides Isosceles Triangle at least 2 congruent sides Equilateral Triangle 3 congruent sides Scalene Triangle No congruent sides

  7. Could an isosceles triangle be equilateral? • So is an equilateral triangle always isosceles… or an isosceles triangle always an equilateral triangle?

  8. Classify the following as equilateral, isosceles, or scalene. Isosceles Equilateral

  9. If point M is the midpoint of JL, classify triangle JKM as equilateral, isosceles, or scalene. Explain your reasoning. Find JM. 0.75 0.75 M is the midpoint. 0.75 JM + ML = JL JM + JM = 1.5 Def. Of Midpoint 2(JM) = 1.5 JM = 0.75 Triangle JKM is an equilateral triangle with all sides 0.75 units.

  10. Classify triangle KML as equilateral, isosceles, or scalene. Explain your reasoning. Isosceles since two sides are congruent (0.75).

  11. Find the measures of the sides of isosceles triangle ABC. 4x + 1 = 5x – 0.5 Since the figure shows the sides equal 1 = x – 0.5 1.5 = x AC = 7 BC = 7 AB = 12.5 AC = 4x + 1= 4(1.5) + 1 = 7 BC = 5x – 0.5 = 5(1.5) – 0.5 = 7 AB = 9x – 1 = 9(1.5) – 1 = 12.5

  12. Find the measures of the sides of equilateral triangle FGH. Since all sides are equal any 2 of the 3 sides can be set equal. 2y + 5 = 3y – 3 5 = y – 3 8 = y FG = FH = GH = 21 FG = 2y + 5 = 2(8) + 5 = 21 FH = 5y – 19 = 5(8) – 19 = 21 GH = 3y – 3 = 3(8) – 3 = 21

  13. Homework • Pg. 238 1 – 14 all, 16 – 44 EOE, 78 – 84 E

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