Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
Objective: to investigate the sum of the angles in a triangle. Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
EXPLORE - Page 146 – You will need a ruler, scissors and a protractor. Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
EXPLORE - Page 146 – You will need a ruler, scissors and a protractor. ➤ Your teacher will give you a sheet with 3 triangles to match each description below: NAME them correctly! a triangle with all acute angles. Label the vertices (corners) A, B, and C. a triangle with one right angle. Label the vertices (corners) D, E, and F. a triangle with one obtuse angle. Label the vertices (corners) G, H, and I. Label them correctly Use a protractor to measure the angles in each triangle. Record the measures inside the triangle at each angle. ➤ With your extra copy, cut out one of the triangles. Cut off its angles. Place the vertices of the three angles together so adjacent sides touch. What do you notice? ➤ Repeat the activity with the other two triangles. Tape one example to the back of the page. What can you say about the sum of the angles in each triangle? ➤ Find the sum of the angles in each triangle. Show your work! Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
CONNECT LAW of MATH It does not matter what triangle you measure, one thing is for sure: Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
CONNECT LAW of MATH It does not matter what triangle you measure, one thing is for sure: The sum of the angles in a triangle is always 180° ∟ A + ∟B + ∟C = 180 ° Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
Explore & Connect Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
CONNECT Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
CONNECT Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
CONNECT Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
Obtuse Triangle Right Triangle Acute Triangle CONNECT Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
Obtuse Triangle Right Triangle Acute Triangle CONNECT Angle A = 60° Angle B = 60° Angle C = 60° TOTAL = 180° Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
Obtuse Triangle Right Triangle Acute Triangle CONNECT Angle D = 90° Angle E = 25° Angle F = 65° TOTAL = 180° Angle A = 60° Angle B = 60° Angle C = 60° TOTAL = 180° Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
Obtuse Triangle Right Triangle Acute Triangle CONNECT Angle G = 25° Angle H = 124° Angle I = 31° TOTAL = 180° Angle D = 90° Angle E = 25° Angle F = 65° TOTAL = 180° Angle A = 60° Angle B = 60° Angle C = 60° TOTAL = 180° Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
PRACTICE – Page #2,3,5,7 Hint: If you know 2 out of 3 angles in a ∆, add those 2 and then subtract from 180 to get your 3 rd angle. Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
#2 a) 75° + 50° = 125°, so 180° - 125° = 55° PRACTICE – Page #2,3,5,7 Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
#2 a) 75° + 50° = 125°, so 180° - 125° = 55° b) 90° + 35° = 125°, so 180° - 125° = 55° PRACTICE – Page #2,3,5,7 Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
#2 a) 75° + 50° = 125°, so 180° - 125° = 55° b) 90° + 35° = 125°, so 180° - 125° = 55° c) 110° + 37° = 147°, so 180° - 147° = 33° PRACTICE – Page #2,3,5,7 Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
#2 a) 75° + 50° = 125°, so 180° - 125° = 55° b) 90° + 35° = 125°, so 180° - 125° = 55° c) 110° + 37° = 147°, so 180° - 147° = 33° #3a) 40° + x° + x° = 180°, so 180° - 40° = 140° This means 2 x’s = 140°, so one x is ½ that = 70° PRACTICE – Page #2,3,5,7 Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
#2 a) 75° + 50° = 125°, so 180° - 125° = 55° b) 90° + 35° = 125°, so 180° - 125° = 55° c) 110° + 37° = 147°, so 180° - 147° = 33° #3a) 40° + x° + x° = 180°, so 180° - 40° = 140° This means 2 x’s = 140°, so one x is ½ that = 70° b) 100° + y° + y° = 180°, so 180° - 100° = 80° This means 2 y’s = 80°, so one y is ½ that = 40° PRACTICE – Page #2,3,5,7 Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
#2 a) 75° + 50° = 125°, so 180° - 125° = 55° b) 90° + 35° = 125°, so 180° - 125° = 55° c) 110° + 37° = 147°, so 180° - 147° = 33° #3a) 40° + x° + x° = 180°, so 180° - 40° = 140° This means 2 x’s = 140°, so one x is ½ that = 70° b) 100° + y° + y° = 180°, so 180° - 100° = 80° This means 2 y’s = 80°, so one y is ½ that = 40° c) 70° + z° + z° = 180°, so 180° - 70° = 110° This means 2 z’s = 110°, so one z is ½ that = 55° PRACTICE – Page #2,3,5,7 Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
#2 a) 75° + 50° = 125°, so 180° - 125° = 55° b) 90° + 35° = 125°, so 180° - 125° = 55° c) 110° + 37° = 147°, so 180° - 147° = 33° #3a) 40° + x° + x° = 180°, so 180° - 40° = 140° This means 2 x’s = 140°, so one x is ½ that = 70° b) 100° + y° + y° = 180°, so 180° - 100° = 80° This means 2 y’s = 80°, so one y is ½ that = 40° c) 70° + z° + z° = 180°, so 180° - 70° = 110° This means 2 z’s = 110°, so one z is ½ that = 55° #5) Vegreville, Alberta, is home to the world’s largest known Ukrainian egg. It has 1108 triangular pieces with three angles of equal measure. Find the measure of each angle. Explain your strategy. PRACTICE – Page #2,3,5,7 Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
#2 a) 75° + 50° = 125°, so 180° - 125° = 55° b) 90° + 35° = 125°, so 180° - 125° = 55° c) 110° + 37° = 147°, so 180° - 147° = 33° #3a) 40° + x° + x° = 180°, so 180° - 40° = 140° This means 2 x’s = 140°, so one x is ½ that = 70° b) 100° + y° + y° = 180°, so 180° - 100° = 80° This means 2 y’s = 80°, so one y is ½ that = 40° c) 70° + z° + z° = 180°, so 180° - 70° = 110° This means 2 z’s = 110°, so one z is ½ that = 55° #5) Vegreville, Alberta, is home to the world’s largest known Ukrainian egg. It has 1108 triangular pieces with three angles of equal measure. Find the measure of each angle. Explain your strategy. xº + xº + xº = 180º, So 3 x”s = 180º Divide 180 by 3 = 60º for each angle. PRACTICE – Page #2,3,5,7 Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
#7) Find the measure of the third angle in each triangle described below. Then, draw the triangle. Explain how you found each measure. a) A triangle with two angles measuring 65° and 55° b) A triangle with two equal angles; each measures 40° c) A right triangle with a 70° angle PRACTICE – Page #2,3,5,7 Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
#7) Find the measure of the third angle in each triangle described below. Then, draw the triangle. Explain how you found each measure. a) A triangle with two angles measuring 65° and 55° b) A triangle with two equal angles; each measures 40° c) A right triangle with a 70° angle a) 65º + 55º = 120º. Then, 180º - 120º = 60º PRACTICE – Page #2,3,5,7 Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
#7) Find the measure of the third angle in each triangle described below. Then, draw the triangle. Explain how you found each measure. a) A triangle with two angles measuring 65° and 55° b) A triangle with two equal angles; each measures 40° c) A right triangle with a 70° angle a) 65º + 55º = 120º. Then, 180º - 120º = 60º b) 40º + 40º = 80º. Then, 180º - 80º = 100º PRACTICE – Page #2,3,5,7 Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_
#7) Find the measure of the third angle in each triangle described below. Then, draw the triangle. Explain how you found each measure. a) A triangle with two angles measuring 65° and 55° b) A triangle with two equal angles; each measures 40° c) A right triangle with a 70° angle a) 65º + 55º = 120º. Then, 180º - 120º = 60º b) 40º + 40º = 80º. Then, 180º - 80º = 100º c) 90º + 70º = 160º. Then, 180º - 160º = 20º PRACTICE – Page #2,3,5,7 Name____ 6__ Lesson #6 - Angles in Jan__ a Triangle_