Question Video: Using Theories of Parallel Chords and Angle Relationships to Prove Parallel Chords | Nagwa Question Video: Using Theories of Parallel Chords and Angle Relationships to Prove Parallel Chords | Nagwa

# Question Video: Using Theories of Parallel Chords and Angle Relationships to Prove Parallel Chords Mathematics • Third Year of Preparatory School

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In which of these figures will line segment π΄π΅ be parallel to line segment πΆπ·? [A] Figure A [B] Figure B [C] Figure C [D] Figure D [E] Figure E

02:21

### Video Transcript

In which of these figures will line segment π΄π΅ be parallel to line segment πΆπ·?

In all of these images, segment π΄π΅ and segment πΆπ· are chords inside a circle. And we know that the measures of the arcs between parallel chords of a circle are equal. To find which of these figures has parallel chords π΄π΅ and πΆπ·, weβll need to find the place where the arcs between the two chords are equal in measure. Notice that in all five of these images weβre given three of the four arc measures. So we need to identify the measure of these missing arcs and then compare that measure to the other arc between those two chords.

We know that all the arcs in a circle sum to 360 degrees. And that means our missing arc π΅π· in option (A) will be equal to 360 degrees minus 55 degrees plus 65 degrees plus 185 degrees, which equals 55 degrees. This means arc π΅π· is not equal in measure to arc π΄πΆ. And therefore these chords are not parallel. In figure (B), we have 360 degrees minus 55 degrees plus 65 degrees plus 175 degrees, which equals 65 degrees. Here, arc π΅π· is equal in measure to arc π΄πΆ. And this makes the chords π΄π΅ and πΆπ· parallel. So weβll select option (B). But letβs go ahead and double-check our remaining three missing arcs.

In option (C), arc π΅π· is 64 degrees, which means chords π΄π΅ and πΆπ· are not parallel. In option (D), the arc measure of π΅π· is 70 degrees, which is not equal to the measure of arc π΄πΆ. And in our final example, arc π΅π· measures 55 degrees, which again means that the chords cannot be parallel. By showing that the measure of arc π΄πΆ was equal to the measure of arc π΅π· in option (D), we were able to prove that the line segments π΄π΅ and πΆπ· were parallel by the measure of arcs between parallel chords theorem.

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