Question

The figure below shows two squares ABPQ and ASRC.
Which angle is equal to angle ACQ?

angle SBA

angle CQA

angle BCQ

angle ASB

Answer 1

k

Answer 2

this one is a toughy

Answer 3

tips

Answer 4

I'm pretty sure you want to use a congruency of triangles argument. Can you show that
\(\Delta\)ACQ\(\cong\Delta\)ASB?

Answer 5

hmm

Answer 6

well

Answer 7

AS corresponds to AC?

Answer 8

Right, and they have the same length because ....

Answer 9

hmm

Answer 10

thinking

Answer 11

just look at them

Answer 12

they seem identical to me

Answer 13

just by looking at them

Answer 14

I can't really tell if their lengths are truly congruent

Answer 15

I mean

Answer 16

the answer is obvious

Answer 17

They are the same lenght, and it's easily proven. Hint: ASRC is a square.

Answer 18

well, each of the triangles are half of the squares?

Answer 19

in other words, both triangles half of their squares, which are congruent?

Answer 20

We're just looking at the sides AS and AC. What special about them that makes them the same length? Use the hint.

Answer 21

they both don't begin with diagonals?

Answer 22

they have right angles?

Answer 23

its hard to explain

Answer 24

You'll kick yourself when I tell you.

Answer 25

thas what cal told me also

Answer 26

It's because both AC and AS are sides of the same square. Hence, they must have the same length.

Answer 27

ahhh

Answer 28

thats make perfect sense

Answer 29

and SB and CQ are both diagonals

Answer 30

Now, how about AQ and AB? Why are these congruent?

Answer 31

lol, sides of the same square

Answer 32

now it makes sense

Answer 33

No one ever taught me, though

Answer 34

I learn so much more when someone actually teaches me than by reading an antisocial lesson

Answer 35

Just reading lessons can be pretty tough.

Now we have one more things to show. Can you show that angle QAC=angle BAS?

Answer 36

they bot hshare the same vertex angle

Answer 37

so they are the same in angle measure

Answer 38

I think you're correct in your thinking. Could you perhaps explain it just a little bit clearer?

Answer 39

they share the same square right angle, lol

Answer 40

the middle angle is always the one that determines the angle measure

Answer 41

That works. So now by SAS the triangles are congruent. So by CPCTC, angle ACQ is the same as angle....

Answer 42

yep

Answer 43

which angle is the same as?

Answer 44

ASB

Answer 45

Perfecto

Answer 46

they both share a square angle

Answer 47

right?

Answer 48

a square has angles of 90 degrees

Answer 49

So angle ACQ equals 90 degrees while ASB equals 90 degrees, right?

Answer 50

I might be wrong, though

Answer 51

just wondering

Answer 52

You don't need to find the actual measure, and they aren't 90 degrees.

Answer 53

k

Answer 54

but still

Answer 55

hey are congruent cause of SAS

Answer 56

k

Answer 57

next problem