Question

prove that the triangle is isosceles

Answer 1

Can you tell from the given info which 2 triangles are similar ?

Answer 2

no idea how

Answer 3

Ever heard of similar triangles ? :|

Answer 4

yes but i am not too sure howto do it

Answer 5

hmm
If you are able to prove triangle PQR and triangle STV are similar, then you can conclude angle SVT = anglePRQ which forces your required result.

Answer 6

both have a 90 degree angle

Answer 7

and ? You are also given some info in the question. Use that.

Answer 8

thats where i get confused bc i dont know what to use

Answer 9

use the fact that, PQ/ST = QR/TV

now this information and that angle information is enough to prove both triangles are similar.
Just tell me by which property of similarity they are similar ?

Answer 10

um can you explain a little more

Answer 11

There is nothing more to explain! ._.
what part you didn't understand ?

Answer 12

there are no values to plug into the ratio

Answer 13

@nincompoop

Answer 14

hi :)

Answer 15

hi @nincompoop

Answer 16

Similar triangles have the same shape (which means they have the same 3 angles)
but different sizes.

label the sides this way: a is the name for the shortest side, b the middle, and c for the longest side.

now label the similar triangle's legs this way: A for the shortest leg, B the middle and C the longest.

if we are told the triangles are similar then we know
\[ \frac{a}{A} = \frac{b}{B} = \frac{c}{C} \]


on the other hand, if they tell us
\[ \frac{a}{A} = \frac{b}{B} = \frac{c}{C} \]
then we know the triangles are similar.

also, if they tell us
\[ \frac{a}{A} = \frac{b}{B} \]
and the angle between sides a,b and A,B are equal, we also know the triangles are similar

This last fact is what we use to prove triangle PQR is similar to triangle STV

Answer 17

so just by saying
\[ \frac{PQ}{ST} = \frac{QR}{TV} \]
and the angle between PQ and QR is 90 which equals the angle between ST and TV
tells us the two triangles are similar

Answer 18

ok.....

Answer 19

next, which angle in the little triangle STV matches (corresponds) to the angle PRQ in the big triangle

Answer 20

T..?

Answer 21

let us begin with what the problem is asking - PROVE that the triangles VKR is ISOSCELES. Definition of terms: A triangles is said to be isosceles when two of its sides are of equal length. Since two of its sides have equal length, it also means that two of its angles are equal.

Answer 22

use 3 letters to show an angle, for example STV means put your finger on S, move along the side to T, and then to V. that is the angle. it is 90º

can you find the angle PRQ ? which angle matches it in the little triangle ?

Answer 23

< STV

Answer 24

no, STV is 90 degrees



in the little triangle, go down the slant leg, and then the bottom