Alec's Pythagoras Scribe Post

4. e. 30x30= 900mm
g. 50x50= 2500mm
f. 40x40= 1600mm
The area of e. is 900 square millimeters
The area of g. is 2500 square millimeters
The area of f. is 1600 square millimeters

9. a) 4x4=16 square cm.
2x2= 4 square cm.
3x3=9 square cm.

b) This is not a right triangle because 2 squared + 3squared doesn't equal 4 squared

12. a) a. squared + b. squared = c. squared
20 + 32 = 52 square cm.
b) a. squared + b. squared = c. squared
100 + 576 = 676 square mm.
c) c. squared - b squared = a. squared
90 - 25 = 65 square cm.
When the hypotenuse is there but one of the leg is missing, I figure it out that when you subtract the one of the legs to the hypotenuse, you will get the missing leg.

d) a. squared + b. squared = c. squared
12 + 12 = 24 square cm.

17. a) a. squared + b. squared = c. squared
21 squared + 28 squared = c .squared
441 + 784 = 1225 square cm.
b) a. squared + b. squared = c. squared
12 squared + 5 squared = c.squared
144 + 25 = 169 square cm.

Ryan's Pythagoras Scribepost

5. A right triangle has side lengths of 40mm, 75mm, and 85mm.

a) Sketch the triangle. Draw a square on each side of the triangle.

b) What are the areas of the three squares?

The area for square a, is 1,600mm2 (squared).

The area for square b, is 5,625mm2 (squared).

The area for square c, is 7,225mm2 (squared).

c) Write an addition statement with the areas of the three squares.

a(squared)+b(squared)=c(squared)

40(squared)+75(squared)=85(squared)

1,600(squared)+5,625(squared)=7,225(squared)

7,225mm(squared)=7,225mm(squared)

10. A triangle has side lengths of 120mm, 160mm, and 200mm. Is the triangle a right triangle? Explain your reasoning.

Yes, this is a right triangle because the sum of the area of each leg, is equal to the area of the hypotenuse.

a(squared)+b(squared)=c(squared)

120(squared)+160(squared)=200(squared)

14,400(squared)+25,600(squared)=40,000(squared)

40,000(squared)=40,000(squared)

15. Construction workers have begun to dig a hole for a swimming pool. They want to check that the angle they have dug is 90 degrees. They measure the diagonal as shown to be 9.5m. Is the angle 90 degrees? Explain your reasoning.

No, the angle is not 90 degrees because the sum of the area of each leg, is not equal to the area of the hypotenuse.

19. A right triangle has a square attached to each side. Two of the squares have areas of 10cm(squared) and 15cm(squared). What are the possible areas for the third square? Draw a sketch for each solution.

There is only one possible area for the third square, and that is the sum of the area of each leg: 25cm(squared). There is only one possible area because it is a right triangle.

Hanna's Pythagoras Scribepost

3.For the triangle shown, Kendra wrote
the Pythagorean relationship as
r2 = p2 + q2. Is she correct? Explain.

Kendra is incorrect. Leg²+leg²=hypotenuse². Since the legs are r and q and the hypotenuse is p, it should be r²+q²=p² or q²+r²=p².

8.Is the triangle shown a right triangle?
Explain your reasoning.

The triangle shown is not a right triangle. For this triangle to be a right triangle, the area of the two smaller squares must equal the area of the larger one. The area of the two smaller squares are 40 cm² and 20 cm² and the area of the larger square is 50 cm². 40+20=60 cm². 60 cm² does not equal 50 cm² because it is 10 cm² greater.

11.The side lengths of a triangle are 5 cm,
6 cm, and 8 cm. Determine whether the
triangle is a right triangle. Explain

This is not a right triangle since the sum of the areas of the two smaller squares aren't equal to the larger square. 6²=36 cm², 5²=25 cm², 8²=64 cm². 36+25=61. 61 doesn't equal 64.

16.Baldeep is building a wooden box for
storing coloured pencils. The box will have
rectangular sides that are 12 cm wide and
20 cm long. Show how Baldeep can be sure
the sides are rectangular, without using
a protractor.

To make sure that the sides are rectangular, I think that Baldeep should make a diagonal line on the rectangle to separate it into two triangles and make squares with the length, width, and the diagonal line you made. Baldeep should then measure the diagonal line and find the areas of the squares and add the areas of the two smaller squares together to see if it is equivalent to the area of the larger square. If it's the same, that means that it is a right triangle which makes the other triangle a right triangle too. If both triangles are right triangles, then the sides are rectangular.

Jayvee's Pythagoras Scribe Post

1. Describe using words and symbols, the relationship among the areas of the three squares.


The relationship among the areas of the three squares is that the sum of the 2 smaller squares is equal to the largest square.

6. a. Write and addition statement using the areas of these three squares.
a2 + b2 = c2
144 + 25 = c2
169cm2 = c

b. What is the side length of each square?
5cm, 12cm, and 13cm

c. Describe, using words and symbols, the relationship between the side lengths of each square.
The relationship among the areas of the three squares is that the sum of the 2 smaller squares is equal to the largest square.



13. A small triangular flower bed has a square stepping stone at each of its sides. Is the flower bed in the shape of a right triangle? Explain your reasoning.
It is a right triangle because the hypotenuse(c) is the longest one.

20. A right triangle has sides of 3 cm, 4 cm, and 5 cm. Attached to each side is a semi-circle instead of a square. Describe the relationship between the areas of the semi-circles.

Find the area of the circles then add them like what we do in the triangle to find the hypotenuse. The relationship is that the formula to find the area of the circle that is attached to the hypotenuse is the same as the formula for the triangle.

Homework , November 4th 2010

Homework :

Show you know #1

A triangle has side lengths of 12 cm , 16 cm & 20 cm.

a) What are the area of the three squares that can be drawn on the sides of the triangle ?

b) Is the triangle a right triangle ? Explain

Show you know # 2

The side of a right angle triangle is 9 cm , 12 cm & 15 cm

a) sketch a picture of the triangle. Draw a square on each side of a triangle .

b) what is the area of each square .

c) write an additional statement using the areas of the 3 squares .

Kristel's Triangle Scribe Post

This is a right triangle because it has a right angle (90 degrees).

A triangle has 3 sides. The horizontal and vertical line are the legs.
The diagonal line is called the hypotenuse.

Side b is 3 cm, side a is 4 cm an and side c, the hypotenuse is unknown.

To find how long the hypotenuse is you can measure it with a ruler or use a formula called Pythagorean Theorem.

The formula is a squared + b squared = c squared.

This is how you would use the formula with this right triangle-

a squared + b squared = c squared
(4 cm squared) + (3 cm squared) = c squared
16 cm squared+ 9 cm squared = c squared
25 cm squared = c squared (with square root over both of them
5 cm = c

Scribe 1

Show You Know; Page 82

Write the prime factorization of each number. Which number is not a perfect square? Explain how you know.

a) 45 b) 100


Page 85

Question #1:
Explain how to square the number 7.

To do this, you would take the number 7 and multiply it by itself once.


Question# 5:
5. a) Determine the prime factorization of 4.
b) Is 4 a perfect square? Explain.
c) Draw the square and label its side length.


Question# 10:
Determine the area of a square with each side length.
a) 20 b) 17

Question #16:

Reminder;
Tomorrow, we will be having a math quiz all about square numbers, roots and perfect squares! To know what to do, you must have all math pages complete because it will be based on the textbook work.

Please remember to comment on all the blogs.