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## Honors

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**Honors**• Markers for sale 25 cents • Warm up • ?? Hmwk • Notes Special Right Triangle • Whiteboard practice • Homework Day 5 • “pop” Quiz over perfect squares and triples moved to tomorrow**3**Investigation**7**Investigation**12**Investigation**Investigation**3 7 12 (1) What type of triangle are we dealing with in each figure above? (2) In regards to the lengths of the sides of each triangle, what pattern can you observe in each triangle? Describe the pattern below. Isosceles Right Triangles Length of Leg times = length of hypotenuse**Isosceles Right Triangles Theoremotherwise knows as (45-**45- 90) Triangle Theorem Mathematical Relationship shown visually: 45 x 45 x Mathematical Relationship written as equation:**k =**k 45 9 45 9 Examples of the (45- 45- 90) Finding the Hypotenuse = We cannot simplify this any more, so we say that this is the “EXACT” answer.**Whiteboard examples of the (45- 45- 90)**C = X = 45 45 16 Find X = ? Find c = ? C X**Find x**x = ________ 45 x 45**Find hypotenuse**hypotenuse = ________ 45 45**Find x**x x 9 (C) x = _________**30-60-90 Triangle Investigation**What kind of triangle is this? 10 cm 10 cm 10 cm Equilateral**30-60-90 Triangle Investigation**What are the measures of each of the angles? 10 cm 10 cm 10 cm**30-60-90 Triangle Investigation**What does this do to the vertex angle? Drop a perpendicular from the vertex angle 10 cm 10 cm 10 cm Bisects it.**30-60-90 Triangle Investigation**What does this do to the base? 10 cm 10 cm 5 cm 10 cm 5 cm Bisects it.**30-60-90 Triangle Investigation**This splits the equilateral triangle into two right triangles….. 10 cm 10 cm 5 cm 5 cm Let’s look at just one of them.**30-60-90 Triangle Investigation**Find the missing leg x on your whiteboard 10 cm x 5 cm 5 cm Write the answer on your notes**18 cm**18 cm 18 cm 30-60-90 Triangle Investigation Let’s do another investigation problem**30-60-90 Triangle Investigation**What does this do to the vertex angle? Drop a perpendicular from the vertex angle 18 cm 18 cm 18 cm Bisects it.**30-60-90 Triangle Investigation**What does this do to the base? 18 cm 18 cm 9 cm 18 cm 9 cm Bisects it.**30-60-90 Triangle Investigation**This splits the equilateral triangle into two right triangles….. 18 cm 18 cm 9 cm 9 cm Let’s look at just one of them.**30-60-90 Triangle Investigation**Find the missing leg x on your whiteboard 18 cm x 9 cm 5 cm Write the answer on your notes**18 cm**10 cm Base leg times 5 times = Base leg times 9 times = 9 cm 5 cm Do you see a pattern? Twice base leg 5 times 2 = 10 Twice base leg 9 times 2 = 18**30- 60- 90 Triangles Theorem**Mathematical Relationship visually: Leg opposite 30 = ________ Leg opposite 60 = ________ Hypotenuse = ________ x 30 2x 2x What’s another way to identify the leg opposite 60 degrees? 60 What is another way to identify the leg opposite 30 degrees? x KEY Side!!!!! SHORTER LEG LONGER LEG**30**2x 60 x Mathematical Relationship Written in equation: KEY Side!!!!!**Whiteboard Examples of the 30- 60- 90**h = = 10 30 h 60 5**Whiteboard Examples of the 30- 60- 90**s= 30 10 = s 60 5**Find y**y = _________ You need to know the shorter side first! Remember the shorter side is the key to solving all 30-60-90 triangles! y Now you can find y**Find x**60 30 x = _________ x 18**Find y**60 30 You need to know the shorter side first! Remember the shorter side is the key to solving all 30-60-90 triangles! y = _________ 18 y**Right Triangles in Other Shapes: Find the perimeter. Round**to nearest tenth! 33.9 Perimeter _________ Hint: Where could we “create” a right triangle? 5 45 7 7 45 5 7