Question

Would anyone be willing to help me with geometry?

Answer 1

From the second and third steps, we know that m∠TUV = m∠1 + m∠2. We also know that m∠XWV = m∠3 + m∠4. Since ∠TUV and ∠XMV both measure 90°, we can set their measures equal to each other:

m∠TUV = m∠XMV

or equivalently:

m∠1 + m∠2 = m∠3 + m∠4

Next, we can use the fact that ∠1 ≅ ∠3 to say that m∠1 = m∠3, while allows us to replace one with the other. Here, we'll replace m∠3 with m∠1:

m∠1 + m∠2 = m∠1 + m∠4

Subtracting m∠1 from either side:

m∠2 = m∠4, which implies that ∠2 ≅ ∠4, as we wanted to show.