Answer:
1. UW // TX
2. VX // UY
3. UW ≅ TY ≅ YX
4. YW = [tex]\frac{1}{2}[/tex] 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 = [tex]\frac{1}{2}[/tex] TX
→ Multiply both sides by 2
∴ 2 UW = TX
∴ TX = 2 UW ⇒ (5)
∵ Y is the midpoint of TX
∴ TY = YX = [tex]\frac{1}{2}[/tex] TX
∵ UW = [tex]\frac{1}{2}[/tex] 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 = [tex]\frac{1}{2}[/tex] 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 = [tex]\frac{1}{2}[/tex] TV ⇒ (4)
∵ 2 Δs UYW and XVT
∵ UY = [tex]\frac{1}{2}[/tex] XV
∵ YW = [tex]\frac{1}{2}[/tex] VT
∵ WU = [tex]\frac{1}{2}[/tex] TX
∴ [tex]\frac{UY}{XV}[/tex] = [tex]\frac{UW}{VT}[/tex] = [tex]\frac{WU}{TX}[/tex] = [tex]\frac{1}{2}[/tex]
→ By using the SSS postulate of similarity
∴ ∠TXV ≅∠WUY ⇒ (6)
