Answer:
The correct statements are;
1) ΔBCD is similar to ΔBSR
2) BR/RD = BS/SC
3) (BR)(SC) = (RD)(BS)
Step-by-step explanation:
1) Since RS is parallel to DC, we conclude that;
∠BDC = ∠BRS (Angles formed on the same side of the transversal)
Furthermore;
∠BCD = ∠BSR (Angles formed on the same side of the transversal)
∠CBD = ∠CBD (Reflexive property)
Thus;
ΔBCD ~ ΔBSR by the Angle-Angle-Angle (AAA) similarity criterion.
2) Given that ΔBCD ~ ΔBSR, we obtain;
BC/BS = BD/BR → (BS + SC)/BS = (BR + RD)/BR = 1 + SC/BS = RD/BR + 1
1 + SC/BS = 1 + RD/BR thus, SC/BS = 1 + BR/RD - 1
SC/BS = RD/BR
By inverting both sides we find;
BR/RD = BS/SC
3) From BR/RD = BS/SC, we apply cross multiplication;
BR/RD = BS/SC leads to;
BR × SC = RD × BS → (BR)(SC) = (RD)(BS).
Answer:
Davide is 10 years old.
L'età di Davide è 10.
Step-by-step explanation:
The average ages of Aldo, Bruno, Carlo, and Davide amount to 16 years.
Let’s denote:
x for Aldo's age.
y for Bruno's age.
z for Carlo's age.
w for Davide's age.
The average for all four is 16 years.
This gives us:
Excluding Davide, the average age of the other three is 18. Therefore:
Substituting into the original equation:
Hence, Davide’s age is indeed 10.
L'età di Davide è 10.