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.


Which is the first incorrect statement in Hazel’s proof?
Answer
Statement 4
Statement 5
Statement 6
Statement 7

Answer 1

ANSWER CHECK I THINK IT IS STATEMENT 6

Answer 2

@jim_thompson5910

Answer 3

@jim_thompson5910

Answer 4

any ideas?

Answer 5

hint: look at figure B

Answer 6

Is it statement 4? @jim_thompson5910

Answer 7

look at figure B, what is the area of the 2 squares combined?

Answer 8

i don't know

Answer 9

my original answer was statement 6

Answer 10

what is the area of one square of figure B

Answer 11

@Hero

Answer 12

@Hero is it statement 6?

Answer 13

@Hero

Answer 14

@Hero

Answer 15

@Hero

Answer 16

what is the area of one square of figure B

Answer 17

i don't know, i dont understand this at all

Answer 18

hint: one square looks like this

Answer 19

the area of that square is ???

Answer 20

x to the 4

Answer 21

what is the formula for the area of a square

Answer 22

4x

Answer 23

that's the perimeter, not the area

Answer 24

x to the 2

Answer 25

yep x^2

Answer 26

so what's the area of a square with a side length of y?

Answer 27

y^2

Answer 28

so what's the total area of the two squares

Answer 29

x^2 and y^2

Answer 30

what do you do with those two expressions to get the total

Answer 31

x^2y^2

Answer 32

you do NOT multiply them

Answer 33

what do u do

Answer 34

you have two numbers, what do you do to them to get the total?

Answer 35

add

Answer 36

x^2 + y^2

Answer 37

so it's x^2 + y^2

Answer 38

yep

Answer 39

notice how it's NOT 2x^2 + 2y^2

Answer 40

so statement 5 is correct when it uses x^2 + y^2

but

statement 6 is wrong when it uses 2x^2 + 2y^2

Answer 41

so the first incorrect statement is statement 6

Answer 42

yep

Answer 43

can you help me with another question

Answer 44

sure

Answer 45

Look at the figure.
Make a two-column proof showing statements and reasons to prove that triangle ABD is similar to triangle ABC.

Answer 46

both triangles ABC and ABD share the same angle which is angle A. both triangles have a 45 degree angle. both triangles share the same side AB. ASA postulate. therefore you can prove that:
ΔABD≈ΔACB

this is all i got, im bad with proofs and i need to make it two column

Answer 47

you did great

Answer 48

both of them share angle A, so that's the common or shared angle

Answer 49

can you help me make it a two column proof

Answer 50

they both have a 45 degree angle, so that's another pair of congruent angles

Answer 51

like i don't know how to make the two columns at all

Answer 52

you have 2 pairs of congruent angles, so that's enough into to use the AA similarity theorem to show that the two triangles are similar

Answer 53

how do i start the columns

Answer 54

you cannot prove that they are congruent, but you can prove that they are similar

Answer 55

what's given here?

Answer 56

that the two traingles are similar

Answer 57

no that's what we want to prove, that will be our last step

Answer 58

i don't know whats given

Answer 59

look at the pic

Answer 60

the angles

Answer 61

be more specific

Answer 62

45 degree

Answer 63

so you can start off by saying that angle ABD = 45 and angle BCD = 45 and the reason is given

Answer 64

you could do these 2 on a single line or have one on each line

Answer 65

okay, now what do i put next

Answer 66

so we have one pair of congruent angles

Answer 67

we need one more pair

Answer 68

angles at adb and acd

Answer 69

i mean bdc fr the second one

Answer 70

@jim_thompson5910

Answer 71

we already covered those, what is another pair

Answer 72

bda, and cdb

Answer 73

remember how you mentioned the shared or common angle?

Answer 74

yes it is D

Answer 75

angle D isn't the shared or common angle

Answer 76

IM CONFUSED

Answer 77

THEY SHARE AB

Answer 78

yelling doesn't help

Answer 79

sorry for the caps lol they share a

Answer 80

yes angle A, be more specific what they share

Answer 81

they share the angle a so thats the other A of the ASA postualte