Q2W2 Dropbox 6.4 Special Parallel

For questions 1-3, choose which condition in the box below proves the shape is a parallelogram. Your Problem: 1. Is the following shape a parallelogram? If so, which condition proves it? Answer: 2. Is the following shape a parallelogram? If so, which condition proves it? Answer: 3. Is the following shape a parallelogram? If so, which condition proves it? Answer: Keep going on to next page! ? 4. Which one of the three theorems on the left would you use to fill reason 6 on this proof? Theorems: Your Problem: 4. Which theorem is used to justify step 6 in the following proof? Answer: Dropbox Quarter 2 Week 1 5.5-5.7 Solving Right Triangles Directions: Examples are in red boxes. You complete the problems in blue boxes. When you are finished, save your work and submit it to the Dropbox. Show your work for full credit. Problem #1: Fill in the Trigonometric Ratios below. If you don’t know how to do this problem, look back at unit 5.4. sin? = cos? = tan? = Problem #2Solving a right triangle when given one side and one acute angle. Example: Check out the process for finding all unknown parts of the triangle by using the table below: Your thought process is listed in RED, what you should fill in the chart is listed in BLUE. Given Angle: Given Side Length Unknown Side Length Trig Function Set up and Solve Other Side Other Angle What acute angle are you given? 55o Look at the side with a number. What is that number, and is it the hypotenuse, or the side opposite or adjacent to the given angle? 21 opposite Look at the side with a variable. What is that variable, and is it the hypotenuse, or the side opposite or adjacent to the given angle? X hypotenuse Which trig function uses the two sides stated in the 2nd and 3rd columns? SIN Since Sin?= opp hyp Sin 55 = 21 X Put sin55 over 1 and cross multiply to solve for x Sin55 = 21 1 x X*sin55=21 0.819x=21 X = 21/0.819 X = 25.64 Since x = 25.64, Use the Pythagorean Theorem to find the last unknown side 212+(FM)2=25.642 FM = 14.71 180-90-55 = 35o Now you try: Use the example above to fill in the chart and find the unknown sides and angle of the triangle below. Given Angle: Given Side Unknown Side Trig Function Set up and Solve Other Side Other Angle One more time: Solve for x on the triangle below. (No chart is given to fill out, but use the same thought process! Only solve for x.) Problem #3Solving a right triangle when given two sides. Example: Check out the process for finding all unknown parts of the triangle by using the table below: Your thought process is listed in RED, what you should fill in the chart is listed in BLUE. One Given Side Length Other Given Side Length Trig Function Set up and Solve Other Side Other Angle Look at one side with a number. What is that number, and is it the hypotenuse, or the side opposite or adjacent to angle x? 7 opposite Look at the other side with a number. What is that number, and is it the hypotenuse, or the side opposite or adjacent to angle x? 4 adjacent Which trig function uses the two sides stated in the 1st and 2nd columns? Remember to use an inverse function when solving for an angle! TAN-1 Since ?tan?^(-1) (opp/adj)= x ?tan?^(-1) (7/4)= 60.26o Use the Pythagorean Theorem to find the last unknown side 72+42=(GM)2 GM = 8.06 180-90-60.26 = 29.74o Now you try: Use the example above to fill in the chart and find the unknown sides and angle of the triangle below. D R M One Given Side Length Other Given Side Length Trig Function Set up and Solve Other Side Other Angle One more time: Solve for x on the triangle below. (No chart is given to fill out, but use the same thought process! Only solve for x) Keep going on to next page! ? Your Problem: 5. Find the lengths and angle measures listed in your answer box below. Your Problem: 6. Use the rhombus to solve for the values in the answer box below: X = y = GH = m F = FJ = m H = All done! Hooray! Now save your work and turn it into the Dropbox ?