WEBVTT
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The diagram shows three straight lines: ๐ด๐ต, ๐ถ๐ท, and ๐ธ๐น.
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The line ๐ธ๐น intersects ๐ด๐ต and ๐ถ๐ท.
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Determine whether the line ๐ด๐ต is parallel to ๐ถ๐ท.
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You must give reasons for your answer.
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There are a number of rules for parallel lines that we should recall.
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The first is corresponding angles are equal.
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When we have a single straight line that intersects two parallel lines, these are the ones that look like theyโre enclosed in the letter F.
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Weโre not allowed to say F angles, but itโs a good way to remember them.
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Alternate angles are also equal.
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These are the ones that look like theyโre enclosed in the letter Z.
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Again, weโre not allowed to say Z angles; itโs just a good way to remember it.
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The third rule relates to the angles that look like theyโre enclosed in a letter C.
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These are called supplementary or co-interior and they add to 180 degrees.
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Letโs compare these three rules to our diagram.
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We can see that we have a single straight line that intersects the lines ๐ด๐ต and ๐ถ๐ท.
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These angles look like theyโre enclosed in the letter C.
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If angles ๐ต๐ธ๐น and ๐ท๐น๐ธ do indeed add to 180 degrees, then this will mean that they are supplementary and the two lines ๐ด๐ต and ๐ถ๐ท must be parallel.
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Letโs check this.
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If necessary, we can add 129 and 51 using the column method.
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Nine plus one is 10.
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So we put a zero in the units column and carry the one.
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Two plus five is seven.
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And then, when we add that carried one, we get eight, so looking good so far.
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And then, one add nothing is just one.
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129 plus 51 is indeed 180.
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We can say that the angles ๐ต๐ธ๐น and ๐ธ๐น๐ท were formed by the intersection of a single straight line with the lines ๐ด๐ต and ๐ถ๐ท.
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Since these two angles add to 180 degrees, we can say that theyโre supplementary and the lines ๐ด๐ต and ๐ถ๐ท are indeed parallel.