Suppose you choose a point Q on the bisector of angle XYZ and you draw the perpendicular segment from Q to YX and the perpendicular segment from Q to YZ. What is true about these segments?

1 Answer
CW
Dec 7, 2017

see explanation.

Explanation:

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As shown in the figure, #YW# is the bisector of #angleXYZ, Q# is a point on #YW#. #AQ and BQ# are perpendicular to #YX, and YZ#, respectively.
As #YQ# is the hypotenuse of #DeltaYQA and DeltaYQB#,
#=> AQ=BQ=YQsinalpha#,
Hence, #AQ and BQ# are equal in length. They are congruent.

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