Question

Anyone smart in geometry?

Answer 1

Answer:

b)  Δ RST ≈  ΔUVW : and ratio is   $\frac{5}{6}$

Step-by-step 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, $\frac{RS}{UV} = \frac{10}{12} = \frac{5}{6} \\\frac{RT}{UW} = \frac{15}{18} = \frac{5}{6} \\\implies \frac{RS}{UV} = \frac{RT}{UW} = \frac{5}{6}$

So, Δ RST ≈  ΔUVW

Hence, Δ RST ≈  ΔUVW : and ratio is   $\frac{5}{6}$