Answer:
b) Δ RST ≈ ΔUVW : and ratio is [tex]\frac{5}{6}[/tex]
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, [tex]\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} \\[/tex]
So, Δ RST ≈ ΔUVW
Hence, Δ RST ≈ ΔUVW : and ratio is [tex]\frac{5}{6}[/tex]
