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Warm Up for Section 1.1 (Tuesday, August 7)

45 o. 45 o. 7. Warm Up for Section 1.1 (Tuesday, August 7) Simplify: (1). (2). Find the two missing edge lengths in each triangle: (3). (4). (5). . 45 o. 45 o. 7. Warm Up for Section 1.1 (Tuesday, August 7)

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Warm Up for Section 1.1 (Tuesday, August 7)

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  1. 45o 45o 7 Warm Up for Section 1.1 (Tuesday, August 7) Simplify: (1). (2). Find the two missing edge lengths in each triangle: (3). (4). (5).

  2. 45o 45o 7 Warm Up for Section 1.1 (Tuesday, August 7) Simplify: (1). (2). Find the two missing edge lengths in each triangle: (3). (4). (5).

  3. Work for Answers to WU, Section 1.1 (1). (2).

  4. Special Right Triangles Standard: MM2G1a, b Section 1.1 Day 2 Essential Question:What is the relationship between the lengths of the edges in a 30°–60°–90°triangle?

  5. Investigation 2: With your partner, complete the following regarding equilateralABC where AB =10: Step 1: Label the length of each edge. Step 2: Label the measure of B and C. Step 3: Using a straightedge, draw and label altitude . Step 4: Label the length of and . Step 5: Label the measure of BAD and CAD. Step 6: Label the measure of ADC. Step 7: Using the Pythagorean Theorem, find AD.

  6. a2 + b2 = c2 A 52 + x2 = 102 25 + x2 = 100 75 = x2 30° 30° 10 10 x 60° 60° B C 5 5 D 10

  7. Investigation 2: Note: the two legs of a 30o-60o-90o triangle are NOT equal in measure. The longer leg will always be opposite the ___o angle. The shorter leg will always be opposite the ___o angle. 60 30

  8. R 30° RT ST 12 60° S T 6 Consider the 30o-60o-90o right triangle created from an equilateral triangle pictured at right. (2). The long leg is segment ______ and the short leg is segment _______. (3). Use the Pythagorean Theorem to find RT.

  9. a2 + b2 = c2 62 + x2 = 122 R 36 + x2 = 144 108 = x2 30° 12 60° S T 6

  10. 30° 2x 60° x Summary: In a 30o-60o-90o triangle: Length of hypotenuse = length of short leg times 2 Length of long leg: length of short leg times Length of short leg: half the length of hypotenuse or the length of the long leg divided by

  11. Check for Understanding: Find the missing edge lengths for each triangle: Example 4:

  12. 60o 30o Check for Understanding: Find the missing edge lengths for each triangle: Example 5:

  13. Check for Understanding: Find the missing edge lengths for each triangle: Example 6:

  14. Check for Understanding: Find the missing edge lengths for each triangle: Example 7: 30o 60o

  15. Check for Understanding: Find the missing edge lengths for each triangle: Example 8: 60o 30o

  16. Check for Understanding: Find the missing edge lengths for each triangle: Example 9: 60o 30o

  17. Application problems: (7). Find the exact area of an equilateral triangle whose edge length is 12 cm. Round your answer to the nearest tenth. Recall: A = ½bh. A = ½bh A = ½(12) A = A ≈ 62.4 cm2 60o 12 12 h 60o 60o 6 6 12

  18. Application problems: (8). Find the exact perimeter of square ABDC if FB = 22 meters A B P = 4s P = 4 P = 22 45o F 22 45o D C

  19. 30° 60° Formula Sheet: Length of long leg = length short leg ∙ _____ Length of hypotenuse = length short leg ∙ _____ Length of short leg = length long leg ÷ ______ Length of short leg = length hypotenuse ÷ ______

  20. 10 x 7 Pythagorean Theorem: a2 + b2 = c2 72 + x2 = 102 49 + x2 = 100 x2 = 51 x =

  21. Triangle Sum Property: Sum of interior s = _____ x° 30° 25° x = 180o – 25o – 30o = 125o

  22. 120° Linear Pair: x° x = 180o – 120o = 60o

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