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15 minutes How do you know a triangle is a right triangle and what is rigid motion? Rigid motion – when you reflect, rotate, translate a pre image the image will have the same size and shape! Rigid – it stays the same…strict, won’t budge http://youtu.be/bbYuCj_eM_w http://www.ck12.org/section/UsingCongruent-Triangles Unit 3 Chapters 4.2, 4.3, 4.6 The angle is the right angle and the sides are the hypotenuse and one of the legs Students cannot use the hypotenuse leg (HL) theorem if they know ONLY that the legs are congruent. In this case, they can still prove that the triangles are congruent by SAS The measure of a (n) ___________ of a triangle is equal to the sum of the measures of its two remote (far side) interior angles. The measures of the three angles of a triangle are given. Find the value of x and tell me the angle degrees. (complete both 2a and 2b) ◦ X, 2x, 3x ◦ X + 10, x – 20, x + 25 Explain how you find the missing angle measure in a triangle? Be specific What is the theorem to find the interior angles of a polygon? Describe how it is used with your favorite type of polygon. What theorem will allow you to prove that the last pair of angles is congruent? How can you find distances on a coordinate plane without measuring? Describe & provide an example Problems in book 4.2, 4.3, and 4.6 work on scale model design (due Wednesday) create flip books to understand 5 types of triangle congruency 4th block needs to finish congruency posters or quadrilaterals and present 6-1 3-5 Scale models Do now: define / describe an isosceles & equilateral triangle and Turn to page 357 and attempt #30 What do all these people have in common? What do they each need to build first? (design first) http://www.virtualnerd.com/geometry/simila rity/ratios-proportions/scale-model-scalefactor 3-5-13 Related to text 3.5, 4.1, 4.2, 4.3, 4.5, 4.6, 5.1, 5.4 (congruence) Quadrilaterals 6.1, 6.5 Actual measurements of appropriate object/building 5 points Scale factor / ratio (shown in key) 3 points Unit of measurements (inch/feet) 3points Dilated correctly to see similarity 5 points Color 3 points Quadrilaterals/triangles used 3 points Described the transformation occurring in scale model 3 points Need to consider the location of angles and sides of triangle Proportions & ratios for comparing corresponding sides You may have to consider the definitions and concepts of the different types of angles from unit 1 1) scale model due Friday (unless you are building a 3-D image and then due Tuesday 3/12) 2) congruence problems & quadrilateral problems (due Friday on loose-leaf paper, not in notebook) Pg. 230 lesson check (SSS) all Pg. 238 lesson check 1 – 4 only (ASA) Pg. 263 problems 15 and 25 Two angles of a triangle are x and 10 + x, what is the third angle? What is x? Activating – all the places that geometry is used http://youtu.be/MvDrn384JYA is a triangle a quadrilateral? What is a quadrilateral? (how do you define?) http://youtu.be/3foPrQgZHWE Why do we need scale factors? Go over triangle congruence problems and mid chapter quiz Discuss SSS, SAS, AA, HL, and AAS 1. use a ruler to draw & label any type of triangle on tracing paper (label ABC) 2. use a ruler to carefully measure segments AB and AC. Use a protractor to measure the angle between them, angle A 3. Write the measurements on an index card & swap cards with a classmate. Draw a new triangle using ONLY your classmate’s measurements 4. compare new triangle to your original triangle 5. try to make your classmates' triangle fit exactly on top of your new triangle Questions: 1. Is your new triangle congruent to your original triangle? 2. Conjecture: what seems to be true about 2 triangles when they have 2 congruent sides and a congruent angle between them? 3. Conjecture: At least how many triangle measurements must you know in order to guarantee that all triangles built with those measurements will be congruent? Do now: Use the distance formula to prove triangles ABC and DEF are congruent. Justify your answer A (1,4) B (5,5) C(2,2) D(- 5, 1), E (-1, 0), F (-4, 3) Activating – song about congruence http://www.songsforteaching.com/math/geo metry/proportionscongruenceofshapes.htm Here are the lyrics, can you think of song to act out Pg. 242 AAA, SSA 1. Form a triangle with segment AB and AC. 2. Then construct BC segment 3. Construct a line parallel to BC that intersects AB and AC at points D and E to form triangle ADE 4. Are the two triangles congruent? Can the two triangles be congruent? Scale model due today Problems: pg. 230, 238, 263 4-6 pg. 243 mid chapter quiz And Review Worksheet with problems 1 – 8 (DO NOT WRITE ON WORKSHEETS) SHOW WORK IN YOUR NOTEBOOK!! Create a 6 word phrase/sentence describing triangles, congruence, and/or quadrilaterals Stipulations: you cannot use the following words – today I learned, I enjoyed today, I now know about What you could start with: Geometry deals with: OR Congruence is important because Write legible & big enough so we can see if I post! 1. 2. 3. 4. 5. Cut straws into 3 pieces (4 inch, 5 inch, 6 inch) Thread string thru 3 pieces of straw Pieces of straw can be in any order Bring the 2 ends of the string together and tie to hold triangle in place Compare with your classmate 1. 2. 3. 4. Is your triangle congruent with your classmates’ triangle? Make a conjecture – what seems to be true about 2 triangles in which 3 sides of one are congruent to 3 sides of another? As a class, choose 3 different lengths and repeat steps 1,2 ,3 Are all the triangles congruent? Does this support your conjecture from question 2