This is a classroom blog hub for Grade 8 students at Sargent Park School.
Wednesday, November 10, 2010
Math Scavenger Hunt Station 2
How do you know that the following are Right Triangles? Explain your thinking in words and pictures. Show your work on a white piece of paper and colour it to explain your thinking
a2+b2=c2 20cm2 + 40cm2= 50cm2 (20x20=400)+(40x40=1600)=(50x50=2500) 400cm2 + 1600cm2= 2000cm2 400cm2 + 1600cm2 doesn't equal 2500cm2 It is not a right triangle.
a2+b2=c2 2cm2 + 3cm2= 4cm2 (2x2=4) + (3x3=9)= (4x4=16) 4cm2 + 9cm2= 13cm2 4cm2 + 9cm2= 13cm2 not 16cm2 so it is not a right triangle
Question 8: The triangle is not a right triangle because if you apply a squared plus b squared equals c squared, it says that c=44.72 which is not correct.
Question 8: a² + b² = c² 20cm² + 40cm² = 60cm² 60cm² ≠ 50cm² The triangle is not a right triangle because the legs don't equal the hypotenuse.
Question 9: The areas are of 2(a), 3(b), 4(c) are: a=4cm² b=9cm² c=16cm²
a² + b²= c² 2² + 3²= c² (2x2)+(3x3)= c² 4cm² + 9cm² = 13cm² 13cm² ≠ 16cm² This triangle is not a right triangle because the legs(a and b) don't equal the hypotenuse(c).
a2+b2=c2 20cm2 + 40cm2= 50cm2 (20x20=400)+(40x40=1600)=(50x50=2500) 400cm2 + 1600cm2= 2000cm2 400cm2 + 1600cm2 doesn't equal 2500cm2 The triangle is not a right triangle.
QUESTION 9
a2+b2=c2 2cm2 + 3cm2= 4cm2 (2x2=4) + (3x3=9)= (4x4=16) 4cm2 + 9cm2= 13cm2 4cm2 + 9cm2= 13cm2 not 16cm2 It is not a right triangle because it doesn't have the a²+b²=c².
40 comments:
a2+b2=c2
20cm2 + 40cm2= 50cm2
(20x20=400)+(40x40=1600)=(50x50=2500)
400cm2 + 1600cm2= 2000cm2
400cm2 + 1600cm2 doesn't equal 2500cm2
It is not a right triangle.
a2+b2=c2
2cm2 + 3cm2= 4cm2
(2x2=4) + (3x3=9)= (4x4=16)
4cm2 + 9cm2= 13cm2
4cm2 + 9cm2= 13cm2 not 16cm2 so it is not a right triangle
Station 2:
Question 8:
The triangle is not a right triangle because if you apply a squared plus b squared equals c squared, it says that c=44.72 which is not correct.
Question 9:
The areas of the squares are:
a=9cm
b=4cm
c=13cm
Stations 1 and 2 were also done by Emily.
8.
a2+b2=c2
40cm2+20cm2=50cm2
60cm2 does not 50cm2
9.
a2+b2=c2
2 squared + 3 squared=4 squared
(2x2)+(3x3)=(4x4)
4+9=16
13 does not equal 16
Neither are perfect squares because when you apply them to a2+b2=c2 the answer is not correct.
a2+b2=c2(50cm2)
40cm2+20cm2=60cm2
50cm2 does not equal 60cm2 so it isn't a right triangle.
a2+b2=c2 (c=4cm 4cm2= 16cm2)
3cm2+2cm2=c2
(3cmx3cm)+(2cmx2cm)=c2
9cm2+4cm2=13cm2
16cm2 does not equal 13cm2 so it is not a right triangle.
These triangles are not right triangles because they do not follow the formula.
8. a2=b2=c2
20cm2=40cm2=60cm2
60 doesn't equal 50
9.a2+b2=c2
2cm2+3cm@=4cm2
(2x2)+(3x3)=(4x4)
13 doesn't equal 16
These triangles are not right triangles because when you apply the formula to these triangles the answer isn't right.
Question 8.
a2 + b2 = c2
40cm2+20cm2=50cm2
(40x40)+(20x20)=(50x50)
1600cm2+ 400cm2= 2500
2000 doesnt = to 2500
No Its not a right triangle because a2+b2 doesnt equal to the hypotenuse.
Question 9.
a2+b2=c2
3cm2+2cm2= 4cm2
(3x3)+(2x2)= (4x4)
9cm2+ 4cm2= 16cm2
13cm2 doesnt = to 16cm2
No its not a right tirangle because 9cm2 + 4cm2= 13cm2, the hypotenuse is 16 cm2.
Question 8.
a2 + b2 = c2
40cm2+20cm2=50cm2
(40x40)+(20x20)=(50x50)
1600cm2+ 400cm2= 2500
2000 doesnt = to 2500
No Its not a right triangle because a2+b2 doesnt equal to the hypotenuse.
Question 9.
a2+b2=c2
3cm2+2cm2= 4cm2
(3x3)+(2x2)= (4x4)
9cm2+ 4cm2= 16cm2
13cm2 doesnt = to 16cm2
No its not a right tirangle because 9cm2 + 4cm2= 13cm2, the hypotenuse is 16 cm2.
#8
a²+b²=c²
40cm²+20cm²=50cm²
60cm²≠50cm²
#9
a²+b²=c²
3²+2²=4²
(3x3)+(2x2)=(4x4)
9cm²+4cm²=16cm²
13cm²≠16²
Both of these triangles do not follow the formula (a²+b²=c²) therefore, they are not right triangles.
a2 + b2 = c2
40cm2 + 20cm2 = 60 cm2
60cm2 ≠ 50cm2
It is not a right triangle.
a2 + b2 = c2
3cm2 + 2cm2 = 4cm2
(3x3) + (2x2) = (4x4)
9cm2 + 4cm2 = 13cm2
13cm2 ≠ 16cm2
It is not a right triangle.
#8
a2+b2=c2
20cm2+40cm2=50cm2
60cm2 does not equal 50cm2
It is not a right triangle.
#9
a2+b2=c2
2cm2+3cm2=4cm2
5cm2 does not equal 4cm2
It is not a right triangle.
8.
a2+b2=c2
40cm2+20cm2= 50cm2
It's not a right triangle.
50cm2 does not equal 60cm2
9.
a2+b2=c2
2cm2+3cm2= 4cm2
(2x2)+(3x3)=(4x4)
4cm2+9cm2=16cm2
13cm2 doesn't equal 16cm2
No, it's not a right triangle.
Station 2
8. a2+b2=c2
20cm2+40cm2=50m2
(20x20)+(40x40)=(50x50)
400cm2+1600cm2=2000cm2
2000 does not equal 2500
9.
A=3x3=9cm2
B=2x2=4cm2
C=4x4=16cm2
Both of these are not right triangles.
Question 8:
a²+ b² = c²
40 cm² + 20 cm² = 50 cm²
1600 cm² + 400 cm² = 2500 cm²
2000 cm² does not equal 2500 cm²
It is not a right triangle
Question 9:
a² + b² = c²
2 cm² + 3 cm² = 4 cm²
4 cm² + 9 cm² = 16 cm²
13 cm² does not equal 16 cm²
It is not a right triangle
Question 8:
a²+b²=c²
40cm²+20cm²=50cm²
60cm²≠50cm²
Question 9:
a²+b²=c²
3²+2²+4²
(3x3)+(2x2)=(4x4)
9cm²+4cm²=16cm²
13cm²≠16²
Both of these triangles don't follow a²+b²=c²
so they are not right triangles
8.
a2+b2=c2
40cm2+20cm2=50cm2 (does not equal 50cm2)
40cm2+20cm2=60cm2
not a right triangle
9.
a2+b2=c2
(3x3)+(2x2) =(4x4)
9cm2+4cm2=16cm2 (does not equal 16cm2)
not a right triangle
Triangle 1 is not a right triangle.
a2+b2=c2
40cm2+20cm2 does not equal 50cm2
40cm2+40cm2=60cm2
60cm2 does not equal 50cm2
Triangle 2 is not a right triangle.
a2+b2=c2
3cm2+2cm2 does not equal 4cm2
9cm2+4cm2 does not equal 16cm2
9cm2+4cm2=13cm2
13cm2 does not equal 16cm2
#8
a²+b²=c²
40cm²+20cm²=50cm²
60cm²≠50cm²
#9
a²+b²=c²
3²+2²=4²
(3x3)+(2x2)=(4x4)
9cm²+4cm²=16cm²
13cm²≠16²
Both of the triangles aren't a right triangle because they don't work with a²+b²=c².
Question 8:
a² + b² = c²
40 cm² + 20 cm² = 50 cm²
1600 cm² + 400 cm² = 2500 cm²
2000 cm² does not equal 2500 cm²
Question 9:
a² + b² = c²
2 cm² + 3 cm² = 4 cm²
4 cm² + 9 cm² = 16 cm²
13 cm² does not equal 16 cm²
Both are not right triangles because both sides of the equation do not equal each other.
Question #8.
a²+b²=c²
20cm²+40cm²=50cm²
(20x20)+(40x40)=(50x50)
400cm²+1600cm²=2500cm²
2000cm² does not equal 2500cm²
This is NOT a right triangle.
Question #9.
Square a
area= SxS
area= 2x2
area= 4cm²
Square b
area= SxS
area= 3x3
area= 9cm²
Square c
area= SxS
area= 4x4
area= 16cm²
a²+b²=c²
2²+3²=4²
(2x2)+(3x3)=(4x4)
4+9=16
13 doesn't equal 16.
This is NOT a right triangle.
#8
a²+b²= c²
40cm²+20cm²=c²
1600+400=2000
2000 does not equal 2500(50cm²) so its not a right triangle.
#9
a=9cm²
b=4cm²
c=16cm²
a2+b2=c2
20squared + 40squared= 50squared
400+1600 does not equal 2500cm
It's not a right triangle
4x4=16.squared cm
2x2=4.squared cm
3x3=9.squared cm
#8
a² + b² = c²
20² + 40² = 50²
(20x20) + (40x40) = 50x50
400 cm² + 1600 cm² = 2500 cm²
2000 cm² ≠ 2500 cm²
This is not a right triangle because 2000 cm² does not equal to 2500 cm².
#9
a² + b² = c²
2² + 3² = 4²
(2x2) + (3x3) = 4x4
4 cm² + 9 cm² = 16 cm²
13 cm² ≠ 16 cm²
This is not a right triangle.
Station 2:
8)
a2+b2=c2
40cm+20cm=50cm
50cm2=60cm2
It is not a right triangle.
9)
a2+b2=c2
(3cm)squared+(2cm)squared=(4cm)squared
9cm2+4cm2=16cm2
16cm2=13cm2
It is not a right triangle.
8)
a2+b2=c2
(40x40)+ (20x 20)= 2000cm2
50 x 50 =2500cm 2
2000cm2= 2500 cm2
NOT EQUAL. It is not a right triangle.
9)
a2+b2= c2
( 3x3)+ ( 2x2)= (4x4)
9 4 16
4cm2+ 9cm2 = 13 cm2
13 cm2= 16cm2
NOT EQUAL. It is not a right triangle.
Question 8.
a² + b² = c²
20² + 40² = 50²
(20x20) + (40x40) = 50x50
400 cm² + 1600 cm² = 2500 cm²
2000 cm² ≠ 2500 cm²
It is not a right triangle because 2000 does not equal 2500
Question 9 .
a² + b² = c²
2² + 3² = 4²
(2x2) + (3x3) = 4x4
4 cm² + 9 cm² = 16 cm²
13 cm² ≠ 16 cm²
It is not a right triangle because 13 does not equal 16.
Station 2:
Number 8
a²+b²=c²
40cm²+20cm²=50cm²
60cm² is not equal to 50cm²
Number 9
a²+b²=c²
2²+3²+4²
(2x2)+(3x3)=(4x4)
4+9=16
13 is not equal to 16
Verdict
Neither are right triangles.
8)
a2+b2=c2
20cm2 + 40cm2 = 50cm2
(20x20=400)+(40x40=1600)=(50x50=2500)
400cm2 + 1600cm2 = 2000cm2
2000cm2 = /2500cm2
This is not a right triangle.
9)a2+b2=c2
2cm2 + 3cm2 = 4cm2
(2x2=4) + (3x3=9) = (4x4=16)
4cm2 + 9cm2 = 13cm2
13cm2 = /16cm2
This is not a right triangle.
8). a2+b2=c2
20cm2+40cm2=50m2
(20x20)+(40x40)=(50x50)
400cm2+1600cm2=2000cm2
2000 does not equal 2500
9).
a=9cm-sqaured
b=4cm-sqaured
c=16cm-sqaured
Question 8:
a² + b² = c²
20cm² + 40cm² = 60cm²
60cm² ≠ 50cm²
The triangle is not a right triangle because the legs don't equal the hypotenuse.
Question 9:
The areas are of 2(a), 3(b), 4(c) are:
a=4cm²
b=9cm²
c=16cm²
a² + b²= c²
2² + 3²= c²
(2x2)+(3x3)= c²
4cm² + 9cm² = 13cm²
13cm² ≠ 16cm²
This triangle is not a right triangle because the legs(a and b) don't equal the hypotenuse(c).
a²+b²=c²
40cm²+20cm²=50cm²
(40x40)+(20x20)=(50x50)
1600cm²+400cm²=2500cm²
2000cm²=2500cm²
It's not a right triangle because it doesn't equal.
Areas of the square:
a=9cm²
b=4cm²
c=16cm²
a2+b2=c2(50cm2)
40cm2+20cm2=60cm2
50cm2 does not equal 60cm2 so it isn't a right triangle.
a2+b2=c2 (c=4cm 4cm2= 16cm2)
3cm2+2cm2=c2
(3cmx3cm)+(2cmx2cm)=c2
9cm2+4cm2=13cm2
16cm2 does not equal 13cm2 so it is not a right triangle.
These triangles are not right triangles because they do not follow the formula.
Station 2
8.a2 + b2 = c2
40 cm2 + 20 cm2 = 50 cm2
1600 cm2 + 400 cm2 = 2500 cm2
it is not a right triangle,
1600+400=2000, not 2500
9.Area of 2=4
Area of 3=9
Area of 4=16
a2+b2=c2
40cm2+20cm2=50cm2
(40x40)+(20x20)=2500
1600+400+2000
The triangle is not a right triangle.
a2+b2=c2
3cm2+2cm2=4cm2
(3x3)+(2x2)=13cm2
9+4=13
The triangle is not a right triangle.
QUESTION 8
a2+b2=c2
20cm2 + 40cm2= 50cm2
(20x20=400)+(40x40=1600)=(50x50=2500)
400cm2 + 1600cm2= 2000cm2
400cm2 + 1600cm2 doesn't equal 2500cm2
The triangle is not a right triangle.
QUESTION 9
a2+b2=c2
2cm2 + 3cm2= 4cm2
(2x2=4) + (3x3=9)= (4x4=16)
4cm2 + 9cm2= 13cm2
4cm2 + 9cm2= 13cm2 not 16cm2
It is not a right triangle because it doesn't have the a²+b²=c².
Station 2
8.
a2+b2=c2
20cm2+40cm2=50cm2
It's not a right triangle because 20cm2+40cm2 doesn't equal 50cm2.
9.
a=4cm2
b=9cm2
c=16cm2
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