Video Transcript
Which of the following is true? Option (A) ๐ด๐ต equals ๐ด๐ถ, option
(B) ๐ถ๐ด equals ๐ถ๐ต, option (C) ๐ต๐ถ equals ๐ต๐ด.
In the diagram, we have a triangle
๐ด๐ต๐ถ, weโve got a line ๐ต๐ถ, and weโve got this ray ๐ต๐ด. In the options that weโre given,
weโre really looking to see if thereโs a pair of lines which are equal in
length. Weโre not given any hash marks on
any of the lines, which would indicate that two are equal. So letโs have a look at the angles
instead.
If we use the fact that the angles
on a straight line add up to 180 degrees, then we should be able to work out this
angle ๐ด๐ถ๐ต and this angle ๐ด๐ต๐ถ. Starting with angle ๐ด๐ถ๐ต, we can
write that thatโs equal to 180 degrees subtract 98 degrees. We can work this out by calculating
180 degrees subtract 100 degrees and then adding on two, which would give us a value
of 82 degrees. We can add this value to the
diagram. The next angle, angle ๐ด๐ต๐ถ, must
be equal to 180 degrees subtract 131 degrees. Subtracting 130 degrees and then
another one degree would give us 49 degrees.
Now that weโve found these two
angles in this diagram, we might think that itโs not very helpful. But letโs see if we can have a look
at calculating the other angle in the triangle ๐ด๐ต๐ถ. We should remember that the angles
in a triangle add up to 180 degrees. So weโll have our unknown angle
๐ถ๐ด๐ต plus angle ๐ด๐ถ๐ต, which we worked out as 82 degrees, plus the angle ๐ด๐ต๐ถ,
which we worked out as 49 degrees, all must add to give 180 degrees. This means angle ๐ถ๐ด๐ต plus 131
degrees equals 180 degrees. Subtracting 131 degrees from both
sides of this equation gives us that angle ๐ถ๐ด๐ต is equal to 49 degrees. We can then add that onto our
diagram and see if thereโs anything to notice.
Well, we should hopefully see that
we have in fact got two angles that are the same size. Both of these are 49 degrees. This means that weโve got an
isosceles triangle here in triangle ๐ด๐ต๐ถ. Any triangle that has two equal
angles must have two equal sides. And therefore, itโs an isosceles
triangle. The two sides that are equal will
be this side ๐ถ๐ด and this side ๐ถ๐ต. We can then give our answer that
๐ถ๐ด equals ๐ถ๐ต, which was the option given in option (B).
