Question

Triangle RTS is similar to RDC. In the figure below, we are given

RT = 12

DT = 4

RS = 9

CS = 3

Prove that ST and CD are parallel.
( I will attach the picture of the triangle.)

Answer 1

okayimhere you need to proove that angle rts =rdc

Answer 2

How do I do that?

Answer 3

do u know trigonometry ?

Answer 4

No.. I'm in Geometry right now.

Answer 5

Ok

Answer 6

Then Use ur above data to prove that these triangles are similar !

Answer 7

I am confused on how though../:

Answer 8

they have a common angle ! Can u identify it for me ?

Answer 9

two triangles rdc and rts have a common angle :)

Answer 10

Try identify it

Answer 11

dcs and tsr are the same

Answer 12

the angles

Answer 13

How do you know tht? If u know tht then explain to me

Answer 14

Or is it given in the question !

Answer 15

Well I actually don't know. I think I'm wrong.

Answer 16

No Your right .... but the problem what u know is given to prove.....Now the triangle rds and rts have a common angle R ... So it makes them similar.!

Answer 17

But don't they have to have at least two common angles?

Answer 18

Yes, but you also know the sides length which are in definite ratio....

Answer 19

So they do make triangles similar, dont they ?

Answer 20

So it's a SAS congruence?

Answer 21

No the triangle are similar...... if triangles are similar then angles of one triangle is equal to the other.......

Answer 22

Ohhhhhh, okay.

Answer 23

In Congruence the triangle's side have to be same......But here its visible that they r not Congruent

Answer 24

Do u rmbr the Complementary Angles Property?

Answer 25

Sry, Not Complementary Angle....Alternate Angles !

Answer 26

Yes, I do. So two triangles can be similar as long as the have congruent angles?

Answer 27

Formally speaking, two triangles and are said to be similar if either of the following conditions holds:
1. Corresponding sides have lengths in the same ratio:
i.e. . This is equivalent to saying that one triangle is an enlargement of the other.
2. is equal in measure to , and is equal in measure to . This also implies that is equal in measure to .

When two triangles and are similar, one writes

Answer 28

Triangle 1 ~ Triangle 2

Answer 29

Now What u earlier told me about angles ......is True

Answer 30

If a transversal intersects two parallel lines, then the corresponding angles are congruent.

Answer 31

Now Angle RST = AngleRCD...Use the above Property to derive your answer.

Answer 32

Are U Okay with this Problem ?

Answer 33

I understand, thankyou so much.!

Answer 34

:)

Answer 35

Wait so how does that prove that the lines are parallel?

Answer 36

Because the Angles RST = RCD ....Now they r corresponding Angles...So if Corresponding Angles are Equal then we can derive a conclusion.....That Line must be parallel..Through this THEOREM(I've posted it above Also)
" If a transversal intersects two parallel lines, then the corresponding angles are congruent."


Its Like if y equals x then x equals y. lol

Answer 37

Okay, got it. Thanks again[:

Answer 38

:)