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Check for UnderstandingGeometric Shapes with Given Conditions (Triangles) Question 1: Which of the following could be the lengths of the three sides of a triangle? A. 1 cm, 2 cm, 3 cm B. 3 in, 3 in, 7 in C. 4 ft, 8 ft, 12 ft D. 5 cm, 7 cm, 9 cm Question 2: Jackie is using popsicle sticks of different lengths to make geometric figures. She has one stick that is 5 centimeters long. Which combination of popsicle stick lengths could fit together with the 5centimeter stick to make a triangle? A. 5, 4, 1 B. 5, 7, 9 C. 5, 3, 2 D. 5, 2, 1 Question 3: A triangle has a side 4.5 inches in length, a 44° angle, and a 39° angle. Which of the following statements about this triangle are false ? Select all that apply: A. This triangle is obtuse B. This could be a scalene triangle C. The third angle is 83 D. All three side lengths are 4.5 Question 4: Which of the following triangles CANNOT be drawn? A. Acute isosceles triangle B. Scalene right triangle C. Obtuse isosceles triangle D. Equilateral right triangle HELP HOW TO SOLVE! Question 1: Which of the following could be the lengths of the three sides of a triangle? A. 1 cm, 2 cm, 3 cm B. 3 in, 3 in, 7 in C. 4 ft, 8 ft, 12 ft D. 5 cm, 7 cm, 9 cm RULE: Visualize: ● The SUM of every pair of sides MUST be larger than the third side length ● It helps to imagine the shape you are creating A 1, 2, 3 1 +2 > 3 NO 2 +3 > 1 YES 1 +3 > 2 YES ● the first pair of sides is not larger than the third side length ● this cannot make a triangle B 3, 3, 7 3 +3 >7 NO 3 +7 >3 YES 7 +3 > 3 YES ● the first pair of sides is not larger than the third side length ● this cannot make a triangle C 4, 8, 12 4 + 8 > 12 NO 8 +12> 4 YES 12 +4> 8 YES ● the first pair of sides is not larger than the third side length ● this cannot make a triangle D 5, 7, 9 5 +7 > 9 YES 5 +9 > 7 YES 7 +9 > 5 YES ● the SUM of every pair is larger than the third side length ● this CAN form a triangle Question 2: Jackie is using popsicle sticks of different lengths to make geometric figures. She has one stick that is 5 centimeters long. Which combination of popsicle stick lengths could fit together with the 5centimeter stick to make a triangle? A. 5, 4, 1 B. 5, 7, 9 C. 5, 3, 2 D. 5, 2, 1 RULE: Visualize: ● The SUM of every pair of sides MUST be larger than the third side length ● It helps to imagine the shape you are creating A 5, 4, 1 5 +4 > 1 YES 5 +1 > 4 YES 1 +4 > 5 NO ● the third pair of sides is not larger than the third side length ● this cannot make a triangle B 5, 7, 9 5 +7 > 9 YES 7 +9 > 5 YES 5 +9 > 7 YES ● the SUM of every pair is larger than the third side length ● this CAN form a triangle C 5, 3, 2 5 +3> 2 YES 3 +2> 5 NO 2 +5> 3 YES ● the second pair of sides is not larger than the third side length ● this cannot make a triangle D 5, 2, 1 5 +2 > 1 YES 2 +1 > 5 NO 1 +5 > 2 YES ● the second pair of sides is not larger than the third side length ● this cannot make a triangle Question 3: A triangle has a side 4.5 inches in length, a 44° angle, and a 39° angle. Which of the following statements about this triangle are false ? Select all that apply: A. This triangle is obtuse B. This could be a scalene triangle C. The third angle is 83 D. All three side lengths are 4.5 RULES: Visualize/Label: ● All angles must add to = 180 ● The SUM of every pair of sides MUST be larger than the third side length ● OBTUSE triangles=have an angle greater than 90 ● RIGHT triangles=have an angle that equals 90 ● ACUTE triangles=have all angles l ess than 90 A Triangle Obtuse? TRUE ● FIRSTfind the missing angle! ● HOW? ○ to FIND the third angle…. ■ ADD the two angles you know ■ SUBTRACT from 180 39 + 44 = 83 180 83 = 97 ● Now we know the third angle = 97 Is this OBTUSE YES WHY? ● any triangle with an angle more than 90 = obtuse! B This could be a scalene triangle? TRUE ● We don’t have enough information to determine the side lengths of this triangle ● BUT we do KNOW that all angles of a Scalene triangle are different. Are all three angles in this triangle different? YES So, could this be a scalene triangle? YES C the third angle is 83? FALSE ● to FIND the third angle….. ○ ADD the two angles you know ○ SUBTRACT from 180 39 + 44 = 83 180 83 = 97 Now we know the third angle = 97 D All three side lengths = 4.5? FALSE ● IF all three side lengths were the same, this would be an EQUILATERAL triangle. ● We know all three angles are: ○ 39, 44, 97 So, can all three sides be equal? NO Question 4: Which of the following triangles CANNOT be drawn? A. Acute isosceles triangle B. Scalene right triangle C. Obtuse isosceles triangle D. Equilateral right triangle