Question #9c6b3

1 Answer
Jan 8, 2018

Read below.

Explanation:

Let's draw this case. I made one in Paint.
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Let's draw a line parallel to line AC. We now have:
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Using our rules on angles formed by parallel lines and by their transcendental line, we can label the following:
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We could name the anlge BAC as #x# and Angle BCA as #180-90-x# or #90-x#

Let's consider triangle DBC. We know that the sum of the interior angles of a triangle is 180 degrees or #pi# radians. We do not know the measure of the angle DBC(we name it #y#), so let's write an equation.
#y=180-90-(90-x)# we simplify this to get:
#y=x#
Since we know that #x# is equal to the angle BAC, we now know that angle DBC is congruent to angle BAC.