Question

Complete the following proof.

Given: m ∠XOY = m ∠WOV
m YZ = m ZW
Prove: m XZ = m ZV

Answer 1

Given that m ∠XOY = m ∠WOV then m XY = m WV, because central angles are equal to arcs.

Given: m YZ = m ZW

The addition of arcs XY and YZ make arc XZ, that is: m XY + m YZ = m XZ

The addition of arcs ZW and WV make arc XZ, that is: m WV + m ZW = m ZV

Then, m XZ = m ZV

Answer 2

Explanation:

m ∠XOY = m ∠WOV

so, m XY = m WV --- (i)

{ If angle subtended by two arcs at the center are equal, then length of arc are equal}

m YZ = m ZW ------- (ii) {given}

Add (i) and (ii)

XY + YZ = WV + ZW

XZ = ZV

Hence proved.