Chapter 10 A Special Right Triangles Geometry PAP

Transcription

1 Chapter 10 A Special Right Triangles Geometry PAP Name Period Teacher

2 th Si Weeks MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY Jan 5 7 Student Holiday Teacher Workday Radicals Review HW: Wksht Radicals Review day 1 & 2 Watch Video Pythagorean Theorem 10.1 Working with Pythagorean theorem CW: Activity Wksht 10.1 Give out project HW: Video Similar Right Triangles 10.1 Working with Pythagorean theorem CW: Activity Wksht 10.1 Give out project HW: Video Similar Right Triangles 9. Similar right triangles (MBD) CW: Worksheet 7. Sim. Right Triangles HW: Video Special Right Triangles Special right triangles CW: Wksht day 1 HW: Video Special right triangles CW: Wksht day 1 HW: Video Very Combo day & Very Special Special Right Triangles Quiz CW: Combo Day and Combo day & Very Special Special Right Triangles Quiz CW: Combo Day and Review Recitation Due (Quiz) HW: Finish Review Special Right Triangles Special Special Right Triangles very special worksht very special Wksht No School Test #10 HW: EOC Practice #1 Watch video Trig Day Trig Day 1 CW: Trig Day 1 & Trig Ratio problems HW: Watch Video Trig Day 2 10.Trig Day 1 CW: Trig Day 1 & Trig Ratio Problems HW: Watch Video Trig Day Trig Day 2 Quiz 1 CW: Trig Day 2 HW: Watch Video Trig Word problems Trig Word problems day 1 CW: Trig Word problems 1 and 2 HW: Complete what not finished in class 10.Trig Word problems day 2 Quiz 2 HW: Complete problems not finished in class Review Day Formula Quiz EOC #1 Due Review day Formula Quiz EOC #1 Due Test #11 HW: EOC Practice #2 Watch Video Area of Parrallograms and Triangles Feb Area of para. and Triangles, Heron s Form CW: Area of Para & Heron s HW: Video on Rhombus 1.2 Area of Rhombus, Kites, and Trapezoids Warm up 1 CW: Area of Rhom, Kites, & Trap HW: Complete Workday Area of figures with SRT and Trig Warm up 2 CW: Area with SRT and Trig Workday Area of figures with SRT and Trig Warm up 2 CW: Area with SRT and Trig 1. Perimeter and Area of similar figures Warm up CW: Similar Fig HW: Finish classwork start more & Kites classwork HW: Video Similar Fig. HW: Video Similar Fig Formula Quiz Review More EOC #2 Due Test #12 HW:EOC Practice # Video on Arc Length & Sector Area 11.1 Circumference and Arc Length CW Wrksht Arc Length Sector Area 11.1 Circumference and Arc Length CW: Wrksht Length sector Area 11. Area of Circles and Sectors Warm up 1 CW: Continue from day before Quiz 1. Area of Regular 1. Area of Regular 1. Area of Regular Review Workday Arc Length Polygons day 1 polygons 2 and Polygons 2 and Formula Quiz and Sectors Warm up 2 Warm up Warm up CW: Review CW: Finish Arc length CW: Regular Polygons CW: Regular Polygons CW: Regular Polygons & Sector Area Day 1 2 & 2 & HW: Study HW: Video Area HW: Video Regular HW: Complete HW: Complete Regular Polygons Polygons Day 2 classwork classwork

3 Simplifying and Multiplying Radicals Review Day 1 Simplify the following radicals. Leave answer in radical form. 1) 1 2) ) 0 Name ) 75 5) 12 ) 12 7) 125 ) 00 9) 12 10) 2 11) 21 12) 12 1) ) 20 15) 0 1) 99 17) 275 1) 20 19) 0 20) 2 21) ) 150 2) ) ) 175 2) 27) 250 2) ) 1,000,000 0) 2 1) 0 2) 5 ) 121 Simplify the following radicals. Leave answer in radical form. ) ) 5 0 ) 5 5 7) 10 ) 2 9) ) ) 72 2) ) ) ) 7 21 ) 2 5 7) ) 2 9) ) 5 51) ) 0 5) 5) 1 55) 2 1 5) ) Page 1

4 Worksheet Dividing Radicals Review Day 1 Name Simplify the following radicals. Leave no square root in the denominator, simplify all radical and numbers. 1) 5 2) 5 ) 1 ) ) 2 7 ) 7 7) 5 10 ) ) ) ) ) ) 9 1 1) 0 15) 20 1) 2 17) 2 1) ) ) ) 10 22) 9 2) 1 2) ) 2 2) 1 27) 2) 7 29) ) 7 1) ) 5 ) 2 ) 0 5) ) ) 27 ) 1 9) 25 0) 1 2 1) 1 2) 20 9 Page 2

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7 Worksheet 10.1 Find the length of the hypotenuse, leave answer in simplest radical form. 1) 2) Find the unknown leg length, leave answer in simplest radical form. ) ) Find the area of the isosceles triangle in simplest radical form. 5) ) The given lengths are two sides of a right triangle. All three side lengths of the triangle are integers and together form a Pythagorean triple. Find the length of the third side and tell whether it is a leg or the hypotenuse. 7) 2 and 2 ) 2 and 5 9) 0 and 5 10) 9 and 1 11) 72 and 7 Find the area of the right triangle. Write your answer in simplest radical form. 12) 1) 1) 15) A shipping dock has a mobile ramp that is used to help load and unload cargo from trucks. The ram is 125 inches long and has a base that is 120 inches long. What is the height h or the ramp? Challenge, Find the value of for each 1) 17) 1) Page 5

8 10.1 Part 2 Converse of Pythagorean Theorem Name Do Work on own sheet of paper. Tell whether the triangle is a right triangle. If not a right triangle, then what kind? 1) 2) ) Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as acute, right, or obtuse. ),, 10 5) 5, 7, 9 ), ) 10, 12, 0 ) 1, 0, 9) 1,, 5 10),, 11) 20, 21, 2 12) 1, 10, 12 1) 1,, 50 Graph points A, B, and C. Connect the points to form ABC. Decide whether ABC is right, acute, or obtuse. 1) 15) 1) 17) The sides and classification of a triangle are given below. The length of the longest side is the integer given. What value(s) of make the triangle? 20),, ; right 21),, 12; obtuse 22),, ; acute 2),, 1; right 2),, 10; obtuse 25),, 15; acute Maps The distances between three towns are given in the diagram. 2) Is the triangle ABC formed by the three towns a right triangle? 27) Town B is directly west of town C. Is town A directly north of town C? Page

9 Worksheet 1 Altitude to the Hypotenuse Name 1) If an altitude is drawn to the hypotenuse of triangle BAN below, then name and redraw the similar triangles created. B T A N Find the missing value below: 2) ) B T A 9 10 A N T B N For - find the length of the altitude of right triangle PQR. ) 5) 12 S P Q Q S P 15 R ) Q R P S 0 R Find the geometric mean of the following numbers. 7) 5 and ) 7 and 11 9) and 9 10) 2 and 25 11) and 12) and 2 Page 7

10 For 7-9 find the length of each leg of right triangle GHK. (find GH and HK) 1) H 1) K 9 G ) How far is it across the lake? K G H km Lake km Solve for the variable(s) 2) ) ) 5) ) 7) 5 y 2 +2 Find the geometric mean for the following numbers. ) 2 and 2 9) and 10) and 7 11) 10 and 12) and 50 1) 1 and 25 Page

11 1) The altitude, XR, to the hypotenuse of right WXY divides the hypotenuse into segments that are and 10 cm long. Find the length of the altitude. 15) How far is it across the quicksand? 1 ft? 115 ft 1) The altitude of a right triangle divides the hypotenuse into two segments whose lengths are 9 cm and 1 cm. Find the lengths of the two legs. 17) Find the lengths of GH and HK. G 2 K H Page 9

12 day 1 Name Period Find the value of the missing sides. Leave in rationalized and simplified form. 17 1) 2) ) ) ) ) 7) ) ) 10) 11) 12) ) 1) 15) 1) ) 1) 19) 20) ) 22) 2) 2) Page 10

13 25) 2) 27) 2) ) 0) 1) 2) ) The sides of a square are 12 inches long. What is the length of the diagonal? ) An isosceles right triangle has a hypotenuse of 2 cm. What is the length of the legs of the triangle? 5) A square has a diagonal with the length of meters. What is the length of the sides? ) An isosceles right triangles legs are 10 feet long. What is the length of the hypotenuse? Page 11

14 day 1 Name Period Find the measure of the missing 2 sides for each figure below. Leave answer in rationalized and simplified form. 1) 2) ) ) 5 ) ) ) ) 9) ) 11) 12) 12 1) 1) 15) 9 1) 17) 12 1) Page 12

15 19) 20) 21) ) 2) 2) ) An equilateral triangle sides are 10 inches. What is the length of the altitude? 2) An equilateral triangle has an altitude of cm. What is the length of the sides? 27) In a 90 triangle, the shortest leg is, what is the length of the longest leg and the hypotenuse? 2) In a 90 triangle, the longest leg is, what is the length of the shortest leg and the hypotenuse? 27) In a 90 triangle, the hypotenuse is, what is the length of the legs of the triangle? Find the measure of the missing 2 sides for each figure below. Leave answer in rationalized and simplified form. 2 1) 2) ) 15 ) 5 ) ) 7 9 7) ) 9) 2 0 Page 1

16 10) 11) 12) ) 1) 15) ) 17) 1) 12 2 Draw a picture for each of the following leave answers in rationalized and simplified form. 19) In an equilateral triangle, the sides are 1 7. Find the length of the altitude. 20) In an equilateral triangle, the altitude is 5. Find the length of the sides. 21) In an equilateral triangle, the altitude is 7. Find the length of the sides. 22) In an equilateral triangle, the sides are 10. Find the length of the altitude. 2) In a triangle, the hypotenuse is 15. Find the length of the longest leg. 2) In a triangle, the shortest leg is 21. Find the length of the longest leg. Page 1

17 Very Special Special Right Triangles Practice Find the value of the variables for each special right triangle Name 1) 2) ) ) 5) ) 7) ) 9) 10) Page 15

18 Combo Day Name Period Choose the best method, and then solve for the indicated values. Leave answers in simplified radical form. 1. m = 2. n = m n. t =. c = c 5. AX =. = W t X square WXYZ A Z 1 Y 2 7. y =. = y y = y 9. = 10. = y = y y = y w = = 12. = 7 y = z = 9 z w 90 1 y Page 1

19 1. A square has a diagonal of length cm. Find the length of each side. 1. An equilateral triangle has sides of length 1 cm. Find the length of the altitude 15. Find the value of. 1. Find the value of Find the value of. 1. Find the value of Find the value of, y and z. 20. Find the missing side lengths of heagon RSTUVW. Find the perimeter. S T R W U V Find the missing lengths for each triangle below. 1) 2) ) ) 5) ) 12 Page 17

20 7) ) 9) ) 11) 12) 1) 1) 15) 9 1) 17) 1) ) 20) 21) ) This toy is a series of isosceles right triangles. If AB 2, find AC, BC, CD, CF, BD, DE, EF, and DF. A C F B D E Page 1

21 2) An etension ladder forming a angle with the ground is placed against an outside wall. The top of the ladder touches a window sill that is 12 feet high. To what length is the ladder etended? How far from the wall is the bottom of the ladder? Give answers in radical form and decimal to nearest tenth. ladder Use the picture of the ski lift for feet 2) A ski lift is shown at the right. Find the distance from the bottom of the lift to the top of the lift. 299 feet 25) In the ski lift, find the length of the shortest cable that could be used. Assume that there is no length around the pulleys. 2) In the ski lift, the actual length of the cable is 10,120 feet. About how much slack is in the cable? Review Special Right Triangles Name Period 1. What is the ratio of all triangles? What is the ratio of all triangles? 2. Find the missing sides for each of the following. Leave answer in simplified and rationalized... a 5. c b 1 12 y r p c a h g Page 19

22 v k w u j z d f 17 e 2 t 15 g h 15. y 1. y g h 1. Find the length of the diagonal of a square with a side of length Draw a diagram. 19. Find the length of a side of a square with a diagonal length of Draw a diagram. 20. The length of a side of an equilateral triangle is 12. Find the length of the 20. altitude. 21. The length of the altitude of an equilateral triangle is 9. Find the length of a side At a point 500 miles north of a ship, the shoreline runs east and west. West of that 22. point, the navigator sights a light house at an angle of. How far is the ship from the lighthouse? shoreline 2. A point on the edge of a symmetrical canyon is 500 ft above a river that cuts through The canyon floor. The angle of depression from each side of the canyon to the canyon floor is Find the length of the canyon wall (from the edge to the river). 2. Page 20

23 Use Pythagorean Theorem on the following triangles Decide if the segment lengths form a triangle. If so, would the triangle be acute, right, or obtuse? 27. 1, 21, and , 19, and 2 29., 9, and , 25, and 1 1. A ladder leaning against a wall makes a angle with the ground. The base of the 1. ladder is m from the building. How high above the ground is the top of the ladder? 2. The roof of a house is the shape of an isosceles right triangle. The slope of the roof is 2. 2 feet, what is the height of the roof? 2 2 Find the geometric mean of the following numbers.. 12 and. and and and 0 Use the special properties of an altitude to the hypotenuse to answer the following questions. Pick problems and find the area of the triangle. 7. Find. Find 9. Find Find 1. Find 2. Find 1. Find. Find and y 5. Find and y 1 y 22 y 9 Page 21

24 Dragon Problem Geometry Name Period The following picture is made up of 90 and 90 special right triangles. Look carefully at each to determine which type of triangle they are. The sum of the squares of the variables is the year that China s Ming Dynasty began. What year was it? Answers: a= b= c= d= e= f= g= h= i= j= Work: a 2 = b 2 = c 2 = d 2 = e 2 = f 2 = g 2 = h 2 = i 2 = j 2 = Sum: Due Date Answer: Page 22