Question

XUV is an isosceles triangle with base UV. determine whether XTU=XWV by the HL theorem. Explain your reasiong. The diagram is not to scale.

Answer 1

Answer:

Step-by-step explanation:

Let draw XD ⊥ UV

XV² = XD² + (VW + WD)²

XU² = XD² + ( UT + TD)²

XV = XU (isosceles triangle)

XV² = XU²

=> (VW + WD)² = ( UT + TD)²

=> VW + WD = UT + TD    -eq 1

XT² = XD² + TD²

XW² = XD² + WD²

XT = XW given

XT² = XW²

=>  TD² = WD²

=> TD = WD  - Eq 2

Using Eq 1 & Eq 2

VW = UT

Now in ΔXTU & ΔXWV   XU= XV , XT = XW & VW = UT

so all sides of triangle are same

ΔXTU = ΔXWV

so all corresponding angles are equal.

so  ∠XTU = ∠XWV