Question

The figures below show two different ways of arranging four identical triangles of grey poster board on top of a white square. The square has sides equal to x + y, while the hypotenuse of each triangle is represented by the variable c.

Answer 1

Hazel wrote the following statements to prove that c2 = x2 + y2.

1. Area of the four grey triangles inside figure A = A equals four times the quantity one-half times x times y, which equals 2 times x times y.
2. Area of the white square inside figure A = c2
3. Area of figure A = c2 + 2xy
4. Area of the four grey triangles inside figure B = 4xy
5. Area of the two white squares inside figure B = x2+ y2
6. Area of figure B = x2+ y2 + 4xy
7. Area of figure A = area of Figure B, hence c2 + 2xy = x2+ y2 + 4xy
8. Therefore, c2 = x2+ y2

Which is the first incorrect statement in Hazel’s proof?

Statement 6

Statement 7

Statement 4

Statement 5

Answer 2

@amistre64

@ganeshie8

@zepdrix

@goformit100

@robtobey

@RadEn

@radar

@primeralph

@dan815

@e.mccormick

@Compassionate

@Coolsector

@Ryaan

@CGGURUMANJUNATH

@dpasingh
Pleaseeee help

Answer 3

Please helpp

Answer 4

first of all, which one would seem off to you?

Answer 5

maybe 4?

Answer 6

Maybe 4?

Answer 7

xy+xy = 2xy is the area of the greys, so 4xy is a bad calculation

Answer 8

so i was correct

Answer 9

thats the first mess up i see :)

Answer 10

yay you help is much appreciated!

Answer 11

@amistre64 can I get help with one more question?

Look at the parallelogram ABCD shown below.

Answer 12

The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent.



Statements
Reasons
1
AB is parallel to DC and AD is parallel to BC
definition of parallelogram
2
angle 1=angle 2, angle 3=angle 4
if two parallel lines are cut by a transversal then the alternate angles are congruent
3
triangles ADB and CBD are congruent
if two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle , then the triangles are congruent
4
BD = BD
Reflexive Property
5
AB = DC , AD = BC
corresponding parts of congruent triangles are congruent

Which statement is true about the table?
It is not correct because it provides incorrect sequence of statement 3 and statement 4.

It is accurate because it provides the correct reasons for the statements.

It is accurate because it provides the correct sequence of statements.

It is not correct because it does not provide correct reasons for statement 2 and statement 4.

Answer 13

@amistre64 please may you help

Answer 14

please post new material in a new post.

Answer 15

and im not the proficient at geometry to try to decipher all that :/

Answer 16

okay i will tag you

Answer 17

ganeshia, prolly spelt it wrong, seems to be a wiz at it