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Types of Angles Class: Geometry Grade Level: 9th Unit: Triangles (2) Teacher: Ms. Jamie Davis Common Core State Standards (CCSS) CCSS.Math.Content.HSG-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects Iowa Core Curriculum-Subject Area Standard(s) geometry: understands and applies properties and relationships of geometric figures; representation: creates and uses representations to organize, record, and communicate mathematical ideas connections- recognizes and uses connections among mathematical ideas and how they build on one another to produce a coherent whole communication- organizes and consolidates his/her mathematical thinking through communication representation- creates and uses representations to organize, record, and communicate mathematical ideas 21st Century Skill(s) Information literacy- access and evaluate information; use and manage information Productivity and accountability- manage products and produce results Objectives Students will be able to recognize triangles based on their features. Students will also be able to distinguish between key characteristics of angles and lengths of sides. Essential Question Can I accurately evaluate triangles and identify them based on their properties? Can I produce my own triangle and describe what its characteristics are? Anticipatory Set Yesterday we talked about triangles in regards to the length of their sides. We identified scalene, isosceles, and equilateral triangles. Who can draw a scalene triangle on the board and describe it? Another volunteer for isosceles and equilateral triangles. Today we will be talking about the angles of triangles and how they define the type of triangle they are as well. Teaching: Activities Acute Triangles: What are acute triangles? -all angles are less than 90* -make pun about “a-cute” like “a cute little puppy” emphasizing the little (like less than 90 being little) Show examples: Obtuse Triangles: What are obtuse triangles? -one angle is greater than 90* -Why can’t more than one angle be more than 90*? --angles add up to 180, 90+90=180, which wouldn’t leave an angle for the 3rd triangle, ie: impossible vocabulary: obtuse=big, fat; the angle is wider than 90* show examples Right Triangles: What is a right triangle? -one angle is 90* once again, why can’t more than one angle be 90*? -- 90+90=180, sum of triangle’s angles = 180, not more than 180 what is special about a right triangle? Where do we see right triangles? (pretty much any corner = 90) how do we label the sides of a right triangle? A,b,c sides where c is always the hypotenuse side vocabulary: hypotenuse: the side opposite of the right angle, always the longest side (z=c, x=b, y=a) Something special about right triangles is that you can calculate the length of a side if you already know the length of the other two. This is why it’s important to know which side is the hypotenuse. We can do this by using the Pythagorean Theorem. Pythagorean Theorem: a^2 + b^2 = c^2 Applied: 1^2+1^2=c^2, 2= c^2, sqrt(2)=c 1^2+sqrt(3)^2=c^2 1+3=c^2 4=c^2 c=2 Never fear! We’ll go over this more in a later class, this is just to introduce the topic! Recap: Watch: http://www.youtube.com/watch?v=Uxk60HWQCE&playnext=1&list=PLD6A4ED54B2909A52&feature=results_main Then briefly go over the triangles again before moving on. Closure On a piece of paper, draw a right triangle, obtuse triangle, acute triangle, equilateral, isosceles, and scalene triangle. Be sure to mark what makes it specifically that. Hand in on your way out the door. Independent Practice Each student is assigned two shapes (figured out in advance) based on their understanding from the previous lesson on triangles and where they are at (below, on, or above-target). code: below target= and on target= and above target= and Purpose: Complete 3 of the tasks using the shapes that you are assigned and you must use at least one of both shapes. What’s not completed during class time is to be done at home as homework **See below for attached table of shapes/activities relating. Assessment assess their understanding as they work on the shape choices activity Materials Tape, scissors, paper, pencils Duration Anticipatory set: 10 minutes Teaching Activities: 30 minutes Independent practice/assessment: 45 minutes Closure: 5 minutes Modified from Madeline Hunters Lesson Plan Design Create a house using only right triangles, being sure to mark the length of the sides and the roof must consist of at least 4 triangles. What is the total height of your building? Research other defining characteristics of triangles and how they apply to what we’ve already learned. State everything that you can identify about each triangle: Now do the same using only obtuse triangles with a total length of one side of the roof being 25 and the height up until the roof is 100. Looking around the classroom, find at least 5 obtuse angles, 5 right angles, and 5 acute angles that you can find. Design 4 different triangles, assigning two of their lengths. Use the Pythagorean Thm to solve for the 3rd side. Find someone else in the class that did this choice to exchange triangles and to try and solve for the 3rd side using the Pythagorean Thm as well and see if you both came up with the same answers. Note: what type of triangles do these have to be? Draw a right, obtuse, and acute triangle. Tear each triangle into 3 parts and line the angles up together. Tape together onto another piece of paper. What do you notice about the angles? Create a Venn-Diagram comparing each type of triangle State two occupations that would need to know/understand triangles on a regular basis and why they would. Find the length of the missing side using Pythagorean’s Theorem. Mark each sides’ congruency if it is and label which kind of triangle it is: Research Pythagoras and write a short (2 page) essay describing how he came across his Theorem, when he did, and any other information you are able to provide. Identify each type of triangle: 1) 3) 4) 5) 6) 2) ANSWER KEY N/A- answers may vary Answers may vary the angles form a line because angles add up to 180 examples: architect, engineer, construction worker, artist, etc. Answers vary depending upon which other features they researched. Answers vary depending upon what the lengths are for the given sides that they draw. Venn-diagram F1=10 F2=5 F3=6 F4=3 F1- right, isosceles F2- acute, isosceles F3- obtuse, scalene I- acute, scalene II- right, 2 sides congruent, isosceles III- obtuse, scalene IV- obtuse, scalene 2 page paper 1 equilateral, acute 2 right, scalene 3 isosceles, obtuse 4 equilateral, scalene 5 isosceles, right 6 acute, obtuse