AABC has acute angles and point X is inside AABC. Points P and R are on AB, points T and Q are on BC, and points S and U are on CA so that PQ passes through X and is parallel to AC, RS passes through X and is parallel to BC, and TU passes through X is parallel to BA. Prove that √^ABC| = √|^XPR|+√|AXQT|+√|AXSU|.
AABC has acute angles and point X is inside AABC. Points P and R are on AB, points T and Q are on BC, and points S and U are on CA so that PQ passes through X and is parallel to AC, RS passes through X and is parallel to BC, and TU passes through X is parallel to BA. Prove that √^ABC| = √|^XPR|+√|AXQT|+√|AXSU|.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter4: Quadrilaterals
Section4.3: The Rectangle, Square, And Rhombus
Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...
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Please don't assume that ABC is equilateral triangle because it is not given that it is equilateral.
Transcribed Image Text:AABC has acute angles and point X is inside AABC. Points P and R are on AB, points T
and Q are on BC, and points S and U are on CA so that PQ passes through X and is parallel
to AC, RS passes through X and is parallel to BC, and TU passes through X is parallel to
BA. Prove that √AABC| = √√|AXPR| + √|AXQT| + √|ÄXSU|.
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