Question

Use the figure to complete each statement 1-6. pleaseee help will give brainliest

Answer 1

Answer:

1. UW // TX

2. VX // UY

3. UW ≅ TY ≅ YX

4. YW = $\frac{1}{2}$ 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 = $\frac{1}{2}$ TX

→ Multiply both sides by 2

∴ 2 UW = TX

∴ TX = 2 UW ⇒ (5)

∵ Y is the midpoint of TX

∴ TY = YX = $\frac{1}{2}$ TX

∵ UW = $\frac{1}{2}$ 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 = $\frac{1}{2}$ 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 = $\frac{1}{2}$ TV ⇒ (4)

∵ 2 Δs UYW and XVT

∵ UY = $\frac{1}{2}$ XV

∵ YW = $\frac{1}{2}$ VT

∵ WU = $\frac{1}{2}$ TX

∴ $\frac{UY}{XV}$ = $\frac{UW}{VT}$ = $\frac{WU}{TX}$ = $\frac{1}{2}$

→ By using the SSS postulate of similarity

∴ ∠TXV ≅∠WUY ⇒ (6)