Question

Hi,

Triangle STU is dilated to form new triangle VWX. If angle S is congruent to angle V, what other information will prove that the two triangles are similar?

Side ST is congruent to side VW.

Angle T is congruent to angle V.

Side US is congruent to side XV.

Angle U is congruent to angle X.

Do not give me the answer.

Thank you.

Answer 1

Similarity:
AAA
Ratios of 2 sides inc <
3 sides prop

Answer 2

(NB: AA can be derived from AAA using < sum of Δ)

Answer 3

From that we conclude:
AA needs two information
Ratios of 2 sides inc < needs three information
3 sides prop needs three information

Answer 4

If we concluded that X is congruent to U, then we can say that this triangle is similar by AA.

Answer 5

yep

Answer 6

Hi,

Lets take a short break from that and revamp to this concern

"Side AC = 4, side BC = 6, side DF = 4, and side EF = 6. What side corresponds to side AB and can be used to show that ΔABC ≅ ΔDEF by SSS? (Enter your answer using letters only)"

Now, I would do AC/BC = DF/EF

Then I would plug them in: 4/6 = 4/6

Cross multiply 24 = 24

However, I am confused. What does it mean "what side corresponds to aB"

Wouldn't it be AC and BC that correspond to AB?

Answer 7

@kc_kennylau , get over here ;D

Answer 8

lolz viewing multiple problems at once ain't an easy thing...

Answer 9

Do mine first, and you won't regret it.

Answer 10

DE corresponds to AB

Answer 11

EF corresponds to BC

Answer 12

DF corresponds to AC

Answer 13

I see, I see.

Now, lets turn 180 degrees, and do this:

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It would be 5/7 = b/16

Which would get 8b = 80

Which b = 10

Answer 14

5/8 = b/16

That's what I mean.

Answer 15

http://www.mathwarehouse.com/geometry/similar/triangles/images/sides-of-similar-triangles-are-proportional.png
ok it seems that you cannot use internal ratios...

Answer 16

b/5=16/8

Answer 17

Right. You get 8b = 80

8/80 = 10

B = 10

Answer 18

yep

Answer 19

Hi, @kc_kennylau

http://prntscr.com/2crtdz

Thank you.

Answer 20

work out the ratios of the corresponding sides first?

Answer 21

Demonstrate, please.

Answer 22

10/52=5/26
2.5/13=5/26
12.5/62.5=5/25

Answer 23

therefore EF should be 65

Answer 24

sorry i have to go now :/

Answer 25

Bye! THANK YOU!

Answer 26

@kc_kennylau ,

One more :)

A kite is a quadrilateral with two pairs of adjacent, congruent sides. Prove the two angles between the non-congruent sides are congruent. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.