Question

Anyone smart in geometry?

Answer 1

b) Δ RST ≈ ΔUVW : and ratio is
`(5)/(6)`

Explanation:

Here, the given triangles are:

Δ RST and ΔUVW

Here, ∠U = 32° , ∠R = 32°

Also, UV =1 2 units, UW = 18 units

and SR = 10 units, TR = 15 units

Now, by SIMILARITY CRITERION:

Two triangles are said to be similar if they have their corresponding sides are in SAME RATIO or their corresponding angles ARE EQUAL.

Here, in Δ RST and ΔUVW

∠U = 32° = ∠R

Also,
`(RS)/(UV) = (10)/(12) = (5)/(6) \\(RT)/(UW) = (15)/(18) = (5)/(6) \\\implies (RS)/(UV) = (RT)/(UW) = (5)/(6) \\`

So, Δ RST ≈ ΔUVW

Hence, Δ RST ≈ ΔUVW : and ratio is
`(5)/(6)`