Download Check for UnderstandingGeometric Shapes with Given Conditions

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