Question

Look at the figure.
What is the length, in units, of segment CD?

Answer 1

What rule could you use to prove that the two triangles are similar?

Answer 2

idk SAS

Answer 3

I said similar. Like by AAA
Do you see two parallel lines and another line crossing them?

Answer 4

yes

Answer 5

So which two angles must be equal (besides the two right angles).

Answer 6

C

Answer 7

i mean A and D

Answer 8

Look at this and then come back
http://hotmath.com/hotmath_help/topics/alternate-interior-angles-theorem.html

Answer 9

A and C

Answer 10

which angle is equal to the angle I've labeled \[\theta\]

Answer 11

C

Answer 12

So there are two angles at the vertex labeled C
Which one do you mean?

Answer 13

the one in the other triangle

Answer 14

Great.

Answer 15

alternate interior

Answer 16

Yes.

Answer 17

Now you have shown that these two triangles share the angle we've been discussing, and it's given that they are both right triangles OK?

Answer 18

ok

Answer 19

So what can you say now, based on that?

Answer 20

you can use pythagoreAN theorem?

Answer 21

We don't need it.

Answer 22

Tell me

Answer 23

Suppose I had two triangles, call them T1 and T2.
And suppose I told you, well T1 has a 90 degree angle and (say) a 30 degree angle.
And then I told you that T2 has a 90 degree angles and a 30 degree angle.
What would you say then?

Answer 24

they are special right triangles

Answer 25

and the other angle is 60

Answer 26

Yes!

Answer 27

So the angles if the angles in T1 are 30, 60 and 90 and the angles in T2 are 30, 60 and 90, then what?

Answer 28

u use trigonometric ratio

Answer 29

Don't need trigonometry for this one.
You have two triangles (yours are not 30-60-90) but they share AAA.
Now what?

Answer 30

i honestly dont know

Answer 31

Well, they are similar triangles. ABC and ACD are similar triangles.
You just proved that.

Answer 32

oh ofcaorse i already knew that

Answer 33

OK. So for similar triangles we have equal ratios for the various sides.

Answer 34

mhm

Answer 35

The side labeled 5 and the side labeled 6 are the same in the two triangles, because they lie between the right and angle, and the angle that is alternate interior to parallel line.s