Question

complete the proof that m∠suv + m∠yxz = 180°. statement reason 1 tv || wy given 2 ∠yxz ≅ ∠vux corresponding angles theorem 3 m∠suv + m∠vux = 180° angles forming a linear pair sum to 180° 4 m∠suv+m∠yxz=180

Explanation:

Step1: Identify equal - angled pairs

We know from step 2 that $\angle YXZ\cong\angle VUX$ by the Corresponding Angles Theorem. This means $m\angle YXZ = m\angle VUX$.

Step2: Substitute equal - angle measures

In step 3, we have $m\angle SUV + m\angle VUX=180^{\circ}$. Since $m\angle YXZ = m\angle VUX$, we can substitute $\angle VUX$ with $\angle YXZ$ in the equation $m\angle SUV + m\angle VUX = 180^{\circ}$.

Answer:

By the Definition of congruence (since $\angle YXZ\cong\angle VUX$ implies $m\angle YXZ = m\angle VUX$), we can substitute to get $m\angle SUV + m\angle YXZ=180^{\circ}$. So the reason for step 4 is the Definition of congruence.