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Understanding and Classifying Triangles: A Comprehensive Guide for Students

This educational resource is designed for 7th to 76th-grade students to enhance their understanding of triangles. Learn how to classify triangles by their sides and angles, drawing each type accurately and finding missing angles using the fundamental principle that the sum of angles in a triangle is 180°. Key concepts include equilateral, isosceles, scalene, acute, right, and obtuse triangles. Engage with exercises that reinforce these concepts and build a strong foundation in geometry, meeting California State Standards for mathematics.

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Understanding and Classifying Triangles: A Comprehensive Guide for Students

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  1. 7-76th grade math Triangles

  2. Objective • To classify and draw triangles, and find missing angles in triangles. • Why? To further your knowledge in measurement and geometry and keeping building a strong foundation in MG in HS

  3. California State Standards MG 2.3: Draw … triangles from information about them (e.g., … a right isosceles triangle). AF 1.1 : Write and solve one-step equations in one variable. AF 3.2: Express in symbolic form simple relationships arising from geometry MG 2.0: Identify and describe the properties of two-dimensional figures. MR 2.4: Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

  4. Vocabulary • Triangles • 3 sided figure and the sum of the angles are 180°. Remember that a triangle is ½ a square or rectangle (whose angles measure 360°). • Congruent triangles • Triangles with the same size and shape

  5. Vocabulary • Equilateral triangle • A triangle with all three sides congruent • Scalene triangle • A triangle with no sides congruent (all 3 sides are different) • Isosceles triangle • A triangle with 2 sides congruent sides • Right triangle • A triangle with a right angle (only 1 angle is needed)

  6. Vocabulary • Acute triangle • A triangle with all three angles with acute measures • Obtuse triangle • A triangle with an obtuse angle (only 1 angle is needed) ↓

  7. Classifying Triangles Classified by Sides *Three congruent sides - equilateral triangle *Two congruent sides - isosceles triangle - may be acute, right, or obtuse *No congruent sides - scalene triangle -may be acute, right, or obtuse Classified by Angles *All acute angles - acute triangle - may be equilateral, isosceles, or scalene *One right angle - right triangle - may be isosceles or scalene *One obtuse angle - obtuse triangle -may be isosceles or scalene

  8. How to Find Missing Angles of a Triangle 1) Add the 2 known angles 2) Subtract 180 from Step 1 3) Check work Triangle with known sides 90° and 30°. 90°+ 30° = 120° 180° – 120° = 60° 3rd side = 60°

  9. Try It! Classify each triangle in 2 ways 1. 2. 3. 4. • Scalene, right • Isosceles, acute • Scalene, obtuse • Equilateral, acute

  10. Try Some More! Find the m∠ of the third angle of teach triangle 5) ∠’s: 98°, 40°, ___ 6) ∠’s: 29°, 84°, ___ 7) ∠’s: 72°, 46°, ___ 8) ∠’s: 43°, 25°, ___ 5) 180 – (98 + 40) = 42° Scalene, obtuse 6) 180 – (29 + 84) = 67° Scalene, acute 7) 180 – (72 + 46) = 62° Scalene, acute • 180 – (43 + 25) = 112° Scalene, obtuse

  11. Objective Review • To classify and draw triangles, and find missing angles in triangles. • Why? You have furthered your knowledge in measurement and geometry and keeping building a strong foundation in MG in HS • You can classify and draw triangles according to side and angle measures. By knowing that the sum of the angles of a triangle is 180°, you can find the measure of an unknown angle.

  12. Independent Practice • Complete problems 10-23 • Copy original problem first. • Show all work! • If time, complete Mixed Review: 24-30 • If still more time, work on Accelerated Math.

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