如图,已知∠AOB = 120°,OC平分∠AOB,交直线DE于点F,若∠EFC = 60°,则OA与DE平行吗?请说明理由. 补全以下解题过程:
Understand the Problem
这道题是要求证明两条直线 OA 和 DE 是否平行。已知 ∠AOB = 120°，OC 平分 ∠AOB，∠EFC = 60°。 需要补全解题过程，利用角平分线的定义和已知角度求出相关角度，然后判断内错角或同位角是否相等，从而判断两直线是否平行。
Answer
$∠AOC=\frac{1}{2}∠AOB=60°$, $∠AOC=∠EFC$, $OA||DE$(同位角相等，两直线平行).
Answer for screen readers
解:平行,理由如下: 因为$∠AOB=120°$,$OC$平分$∠AOB$, 所以$∠AOC=\frac{1}{2}∠AOB=60°$。(角平分线的定义) 又因为$∠EFC=60°$, 所以$∠AOC=∠EFC$, 所以$OA||DE$(同位角相等，两直线平行).
Steps to Solve
- Find $∠AOC$
Since $OC$ bisects $∠AOB$, we have $∠AOC = \frac{1}{2} ∠AOB$. Substitute $∠AOB = 120°$ to find $∠AOC$.
$∠AOC = \frac{1}{2} \times 120° = 60°$
- Find the relationship between $∠AOC$ and $∠EFC$
We are given that $∠EFC = 60°$. From the previous step, we found that $∠AOC = 60°$. Therefore, we have $∠AOC = ∠EFC = 60°$.
- Determine if $OA || DE$
$∠AOC$ and $∠EFC$ are corresponding angles. Since $∠AOC = ∠EFC$, we can conclude that $OA || DE$ because corresponding angles are equal.
解:平行,理由如下: 因为$∠AOB=120°$,$OC$平分$∠AOB$, 所以$∠AOC=\frac{1}{2}∠AOB=60°$。(角平分线的定义) 又因为$∠EFC=60°$, 所以$∠AOC=∠EFC$, 所以$OA||DE$(同位角相等，两直线平行).
More Information
When a line intersects two other lines, several angles are formed. If the corresponding angles are equal, then the two lines are parallel.
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