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# Geo1.5 Triangles Lesson

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• Address the right angle mark to represent perpendicularity.
• Discuss how many degrees all three interior angles of a triangle will sum up to.
• Have students identify which angles in triangles XWV and SAM are acute and obtuse.
• Bring up the usage of hash/tick marks from lesson 1.1 to denote congruence. Question whether or not they can be used in this triangle.
• Speak to students about possibly calling the equilateral triangle by another name because it fits in to the classification of an acute triangle. Discuss how if we have an equilateral triangle, all three sides cause all three angles to be congruent – and vice versa.
• Allude to a regular quadrilateral – or a quadrilateral with equal sides and equal angles.
• ### Geo1.5 Triangles Lesson

1. 1. <ul><li>DO NOW </li></ul><ul><li>Name me with proper notation! </li></ul><ul><li>How many sides, vertices, & diagonals do I have? </li></ul><ul><li>Name one pair of: </li></ul><ul><ul><li>consecutive sides </li></ul></ul><ul><ul><li>consecutive angles </li></ul></ul><ul><ul><li>consecutive vertices </li></ul></ul>AIM 1.5 : How can we classify triangles? REMINDER! Quiz #1 on MONDAY ! September 11 th , 2009 What did the hypotenuse say to the other sides? Nice legs!
2. 2. <ul><li>Take out last night’s homework on polygons for review. </li></ul><ul><li>Any questions? </li></ul><ul><ul><li>I understood that… </li></ul></ul><ul><ul><li>I had a hard time with… </li></ul></ul><ul><ul><li>I don’t understand how to… </li></ul></ul><ul><ul><li>I learned that… </li></ul></ul>HW Review Triangles & Food!
3. 3. Classifying Triangles <ul><li>Create a chart in your notebook to organize the various definitions and drawings that we will be taking down as part of this lesson. </li></ul>So what was our definition of a triangle again?!?!?!
4. 4. Triangles <ul><li>A triangle is a three sided polygon with 3 vertices and no diagonals. </li></ul><ul><ul><ul><li>All of this was from our DO NOW! </li></ul></ul></ul><ul><li>Have you heard of these types of triangles before? </li></ul><ul><ul><li>Right, acute, obtuse, scalene, equilateral, and isosceles? </li></ul></ul>
5. 5. Come up with the definitions! <ul><li>In groups of two or three, you will look at page 60 and 61 to look at six different types of triangles. </li></ul><ul><li>Your goal is to come up with ‘good’ definitions that describe each type of triangle. </li></ul><ul><li>Make sure you sketch the triangles into your notebook! </li></ul><ul><li>Try your best, we will come together as a group to go over your definitions. </li></ul>
6. 6. Right Triangles <ul><li>Definition: </li></ul><ul><ul><li>A right triangle has one right angle. </li></ul></ul><ul><li>Sketches: </li></ul>
7. 7. Acute Triangle <ul><li>From our lesson last week, what is an acute angle? </li></ul><ul><li>Definition: </li></ul><ul><ul><li>An acute triangle has three acute angles. </li></ul></ul><ul><li>Sketches: </li></ul>72° 58° 50° 84° 46° 50°
8. 8. Obtuse Triangle <ul><li>What’s an obtuse angle? </li></ul><ul><li>Definition: </li></ul><ul><ul><li>An obtuse triangle has one obtuse angle. </li></ul></ul><ul><li>Sketches: </li></ul>135° 98° X W V M A S
9. 9. Scalene Triangle <ul><li>Definition: </li></ul><ul><ul><li>A scalene triangle is a triangle with no congruent sides. </li></ul></ul><ul><li>Sketches: </li></ul>Can we use tick/dash marks to denote congruence of sides in triangle XWV? 28” 20” 11” X W V
10. 10. Equilateral Triangle <ul><li>Definition: </li></ul><ul><ul><li>An equilateral triangle has three congruent sides and three congruent angles. </li></ul></ul><ul><li>Sketches: </li></ul>Can we use any tick/hash marks to denote congruence of sides and angles in these triangles? 60° 60° 60° 3’ 3’ 3’
11. 11. Equilateral Triangle = Regular Polygon? <ul><li>Remember polygons? </li></ul><ul><ul><li>Well, an equilateral triangle is actually what we call a regular 3-sided polygon. This is because it is a polygon that has congruent sides and congruent angles. </li></ul></ul><ul><ul><li>We can also have regular quadrilaterals, pentagons, hexagons, heptagons, etc… </li></ul></ul><ul><ul><li>What might a regular quadrilateral be called? </li></ul></ul>
12. 12. Isosceles Triangle <ul><li>Definition: </li></ul><ul><ul><li>An isosceles triangle has at least two congruent sides. </li></ul></ul><ul><li>Sketches </li></ul>J A M F O E
13. 13. Isosceles Triangles (continued) <ul><li>Let’s analyze an isosceles triangle more closely… </li></ul>Vertex Angle Base Angles Base
14. 14. Guided Practice <ul><li>Page 62, #1 - 9 </li></ul>
15. 15. <ul><li>What type of triangles can you classify in this painting? </li></ul><ul><ul><li>Kazuya Akimoto </li></ul></ul><ul><ul><li>“ Rising Blue Triangles” </li></ul></ul><ul><ul><li>pastel 55×43cm </li></ul></ul><ul><ul><li>2003 </li></ul></ul>
16. 16. <ul><li>Triangles are often found in a lot of architectural designs. For example, this is a structure over a bridge that contains triangles. </li></ul>
17. 17. YES… WE CAN!!!
18. 18. <ul><li>How do we classify three sided polygons? </li></ul><ul><li>What pieces of information do we need to know to classify triangles appropriately? </li></ul><ul><li>LOOKING AHEAD… </li></ul><ul><ul><li>On Monday, we will take the first unit quiz. Be sure to study! </li></ul></ul><ul><li>HOMEWORK… </li></ul><ul><ul><li>Complete worksheet. </li></ul></ul>In closing…