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Understanding Triangle Vocabulary and Classifications: Homework and Quiz Preparation

In this lesson, we explore the essential vocabulary related to triangles, including assumptions and classifications based on sides and angles. Students will learn crucial distinctions such as equilateral, isosceles, scalene, acute, obtuse, and right triangles, alongside practices that reinforce their understanding through sketches and constructions. The lesson also emphasizes the importance of not making assumptions based on visual diagrams. Homework tasks (1.5/1-14, 17-21, 24-26) prepare students for an upcoming quiz on lessons 1.3 to 1.5 taking place this Friday.

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Understanding Triangle Vocabulary and Classifications: Homework and Quiz Preparation

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  1. Lesson1.5 – Triangle Vocabulary Homework: 1.5/1-14, 17-21, 24-26 Quiz Friday on Lesson 1.3 – 1.5

  2. Assumptions • To assume something is to accept it as true without facts or proof. • When looking at a diagram, be careful notto assume anything

  3. Things you may assume • Lines are straight • If two lines intersect, they intersect at one point • Points on a line are collinear • All points shown in a diagram are coplanar unless additional planes are shown

  4. Things you may NOT assume Just because they look: • parallel • two lines or segments are NOT necessarily parallel • perpendicular • two lines are NOT necessarily perpendicular • Congruent • pairs of angles, segments, or polygons are NOT necessarily congruent

  5. All CONGRUENT, PARALLEL, PERPENDICULAR parts MUST be MARKED

  6. Classifying Triangles • A triangle has three sides and three angles • The three angles always add to 180° • There are special names given to triangles that tell how many sides or angles are equal. • There can be 3, 2 or no equal sides/angles: • Sides: Equilateral, Isosceles and Scalene • Angles: Acute, Right, Obtuse, and Equiangular

  7. Classify by Sides Equilateral Triangle Three equal sides Isosceles Triangle Two equal sides Scalene Triangle No equal sides

  8. Classify by Angles Acute Triangle All angles are between 0°and 90° Right Triangle Has exactly one right angle (=90°) Obtuse Triangle Has one angle between 90° and 180° Equiangular Triangle Three equal angles, always 60°

  9. Combining the Names • Sometimes a triangle will have two descriptive names. • One for angles & one for sides For example: • Right Isosceles Triangle • It has a right angle (90°), and also two equal angles • Can you guess what the measure of the equal angles are?

  10. Can you have an: • YES • NO • NO • YES • NO • Scalene right triangle? • Obtuse acute triangle? • Equiangular scalene triangle? • Isosceles right triangle? • Equilateral obtuse triangle?

  11. Levels of making a picture • Sketch • To create the picture with only a pencil; freehand • Draw • To use measuring tools: ruler and protractor • Construct • To use construction tools: compass and straightedge These terms will determine what tools, if any, you are required/allowed to use.

  12. Sketch, mark, and label 1. 2.

  13. 1. M N A 2. O U P Y

  14. Draw, mark, and Label • ΔBAD with BA = 2.5 cm, m<A = 75˚ • Right scalene ΔHOP with right angle P, PO = 4cm, PH = 2cm. 3. 4.

  15. D 3. B 75˚ A 2.5cm 4. H 2cm P O 4cm

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