SOLUTION: complete the following proof related to the figure below.
the figure is a triangle with a line down the middle, the top is labeled T, angle on the right is S, angle on the left
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-> SOLUTION: complete the following proof related to the figure below.
the figure is a triangle with a line down the middle, the top is labeled T, angle on the right is S, angle on the left
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Question 626389: complete the following proof related to the figure below.
the figure is a triangle with a line down the middle, the top is labeled T, angle on the right is S, angle on the left is R and the bottom of the segment that goes through the middle is labeled Q.
Given: segment TQ bisects angles RTS, angle R=angles S Prove: segment TQ is perpendicular segment RS Answer by solver91311(24713) (Show Source):
The sum of the measures of the internal angles of all triangles is 180, so since mRTQ = mSTQ (defn bisector) and mR = mS (given), mRQT = mSQT (set up an equation and use Transitive Equality. But RQS is a straight angle and mRQS = mRQT + mSQT. The defn of a straight angle and a little algebra says that mRQT = mSQT = 90 degrees. Hence TQ RS by defn perpendicular.
John
My calculator said it, I believe it, that settles it
