Answer:
1. UW // TX
2. VX // UY
3. UW ≅ TY ≅ YX
4. YW =
TV
5. TX = 2 UW
6. ∠TXV ≅∠WUY
Step-by-step explanation:
The line segment joining the midpoint of two sides of a triangle is parallel to the third side and equal to half its length
In Δ XVT
∵ U is the midpoint of VT
∵ W is the midpoint of VX
∵ XT is the 3rd side of the triangle
→ By using the rule above
∴ UW // TX ⇒ (1)
∴ UW =
TX
→ Multiply both sides by 2
∴ 2 UW = TX
∴ TX = 2 UW ⇒ (5)
∵ Y is the midpoint of TX
∴ TY = YX =
TX
∵ UW =
TX
∴ UW ≅ TY ≅ YX ⇒ (3)
∵ U is the midpoint of VT
∵ Y is the midpoint of XT
∵ VX is the 3rd side of the triangle
→ By using the rule above
∴ UY // VX
∴ VX // UY ⇒ (2)
∴ UY =
VX
∵ W is the midpoint of VX
∵ Y is the midpoint of XT
∵ TV is the 3rd side of the triangle
→ By using the rule above
∴ YW // TV
∴ YW =
TV ⇒ (4)
∵ 2 Δs UYW and XVT
∵ UY =
XV
∵ YW =
VT
∵ WU =
TX
∴
=
=
= 
→ By using the SSS postulate of similarity
∴ ∠TXV ≅∠WUY ⇒ (6)
The answer is 7 pounds because 16 ounces is equal to 1 pound so 7 pounds times 1 pound would equal 7 pounds.
Answer:
a. x = 8
b. m<B = 140
Step-by-step explanation:
a.
m<A = m<B
40 = 5x
x = 8
b.
m<A + m<B = 180
m<B = 180 - m<A
m<B = 180 - 40
m<B = 140
Answer:
80 members
Step-by-step explanation:
Let the band members be= b and the chorale members= c
Then, according to question, b=c+30 and 
⇒
⇒
⇒
⇒
Now, substituting the value of b=c+30, we get
⇒
⇒
⇒
⇒
Therefore, 

Therefore, there are 80 members in the band.