Question

Given:
Square with side c.
All four interior triangles are right triangles.
All four interior triangles are congruent.
The interior quadrilateral is a square.

Prove:
a2 + b2 = c2

Answer 1

When written in the correct order, the paragraph below proves the Pythagorean Theorem using the diagram.

Let a represent the height and b represent the base of each triangle.

The area of one triangle is represented by the expression One halfab.

(1) The length of a side of the interior square is (a – b).

(2) The area of all four triangles will be represented by 4 • One halfab or 2ab.

(3) The area of the interior square is (a – b)2.

(4) By distribution, the area is a2 – 2ab + b2.

The area of the exterior square is found by squaring side c, which is c2, or by adding the areas of the four interior triangles and interior square, 2ab + a2 – 2ab + b2.

Therefore, c2 = 2ab + a2 – 2ab + b2.

Through addition, c2 = a2 + b2.

Answer 2

Which is the most logical order of statements (1), (2), (3), (4) to complete the proof?

(2), (1), (4), (3)

(1), (2), (3), (4)

(1), (2), (4), (3)

(2), (1), (3), (4)

Answer 3

hey king geogre

Answer 4

this is another geometry problem that has been giving me trouble :(

Answer 5

you think that you can help?

Answer 6

hey guys

Answer 7

this is another tough geometry problem

Answer 8

you think you guys can help me with this challenge?

Answer 9

First off, which order do you think is correct and why?

Answer 10

hmm

Answer 11

One seems to go first

Answer 12

so that eliminates choices 1 and four

Answer 13

I agree so far.

Answer 14

so 2 would have to go next

Answer 15

then 3 would have to go third

Answer 16

and 4 sums up the areas

Answer 17

Perfect.

Answer 18

wow...

Answer 19

That wasn't so hard when you guided me...

Answer 20

Exactly. Most of these you just need a push in the right direction.

Answer 21

ty

Answer 22

and the duplicate I chose for question 4 on that last assignment was incorrect

Answer 23

remember the question with two identical answer choices?

Answer 24

yup.

Answer 25

k...

Answer 26

hmm...

Answer 27

Which did you guess?

Answer 28

I guessed the third one on the question 4 thing

Answer 29

I guess I answered the wrong duplicate :(

Answer 30

sad day :(

Answer 31

I need to ask you something

Answer 32

is f squared= a squared + b squared an example of the reflexive property of equality?

Answer 33

No. I wouldn't think so.

Answer 34

really?

Answer 35

a=a

Answer 36

f squared= a squared +b squared

Answer 37

a=a would be an example.

Answer 38

3=3

Answer 39

25=9+16

Answer 40

25=25?

Answer 41

It would not be substitution, right?

Answer 42

anything that's an example of reflexive is something that looks like \(a=a\). Which of these look like that?

Answer 43

well...

Answer 44

not f squared=a squared plus b squared

Answer 45

could it be substitution instead?

Answer 46

I'm not sure what that one is without more context. However, substitution sounds like it might be correct.

Answer 47

whats an example of substitution?

Answer 48

(A) + B = 12
(2B) + B = 12
3B = 12
B = 4

Answer 49

thats one example

Answer 50

\(a=g+c\), \(g=h \implies a=h+c\). Is one example. What you gave is another example.

Answer 51

so f squared= a squared plus b squared must be an eaxample, right?

Answer 52

What are the other options?

Answer 53

Reason #1 - Reflexive Property of Equality
Reason #2 - SSS Postulate

Reason #1 - Substitution
Reason #2 - SAS Postulate

Reason #1 - Substitution
Reason #2 - SSS Postulate

Reason #1 - Reflexive Property of Equality
Reason #2 - SAS Postulate

Answer 54

I'm thinking the second choice

Answer 55

they are trying to prove that a triangle has a right angle

Answer 56

thats why I go for SAS

Answer 57

Given: In ∆ACB, c2 = a2 + b2.
Prove: ∆ACB is a right angle.

Complete the flow chart proof with missing reasons to prove that ∆ACB is a right angle.

Answer 58

Triangles ACB and DFE are shown below.

Answer 59

anything?

Answer 60

First one, reason 1 is definitely substitution. However, I would use SSS instead SAS because you're given 3 sides, and not angles.

Answer 61

k

Answer 62

So you are thinking choice three?

Answer 63

That's what I would choose.

Answer 64

k

Answer 65

ty

Answer 66

you're welcome.

Answer 67

ehhh

Answer 68

can you help me with the last geometry problem of the day?

Answer 69

just one more...

Answer 70

just one more...

Answer 71

Given: In ∆ABC, segment DE is parallel to segment AC .
Prove: BD over BA equals BE over BC

Answer 72

The two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally.

Answer 73

Statement 1:
Line segment DE is parallel to line segment AC

Answer 74

Reason is given

Answer 75

Statement 2:
Line segment BA is a transversal that intersects two parallel lines

Answer 76

Reason: Conclusion from statement 1

Answer 77

3. Statement and Reason blank

Answer 78

Angle B is congruent to Angle B(4.)

Answer 79

Reason: Reflexive property of equality

Answer 80

Triangle ABC is similar to triangle DBE

Answer 81

Reason: Angle-Angle(AA) Similarity Postulate

Answer 82

Statement and Reason for 6. is unknown

Answer 83

Complete the proof by entering the correct statements and reasons.

Answer 84

hey agent

Answer 85

Are there any options for the statements/reasons?

Answer 86

sadly no :(

Answer 87

I have to fill them in

Answer 88

any suggestions or tips?

Answer 89

what say you monkey?

Answer 90

for 6, it's pretty easy. It's the very last statement in the proof. What does this mean it has to be?

Answer 91

BD over BA equals BE over BC

Answer 92

lol

Answer 93

and the reason is

Answer 94

hmm...