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Makumajon · 09-02-2008, 06:26 AM

While applying the similar triangle properties rule, be careful to compare a side of one triangle with its appropriate counterpart from the other triangle. Here, consider the two split triangles: QMP & QMR (M is the point in which the perpendicular intersects the base PR.

QMP vs. QMR:
QMP=QMR...(1) (because each angle is 90 degree)
Angle QPM=Angle RQM...(2) (because each angle is complementary to angle PQM)
Angle PQM=Angle QRM...(3) (because each angle is complementary to angle RQM)

Once you have identified the equal angles, you now apply the side ratio relationship. You must choose side opposite to corresponding angles.

(1) gives you PQ/RQ
(2) gives you QR/RM
(3) gives you PM/QR.

So, PQ/RQ=QR/RM=PM/QR. Here you do not need to first ratio.

So, QR/RM=PM/QR
=> PM*RM=QR^2. This relationship in split right triangles is so favorite among GMAT, GRE, SAT, CAT, MBA tentmakers that you can memorize it.

09-02-2008, 06:26 AM	#9 (permalink)
Makumajon TestMagic Guru Join Date: May 2008 Location: Bangladesh Posts: 1,040	While applying the similar triangle properties rule, be careful to compare a side of one triangle with its appropriate counterpart from the other triangle. Here, consider the two split triangles: QMP & QMR (M is the point in which the perpendicular intersects the base PR. QMP vs. QMR: QMP=QMR...(1) (because each angle is 90 degree) Angle QPM=Angle RQM...(2) (because each angle is complementary to angle PQM) Angle PQM=Angle QRM...(3) (because each angle is complementary to angle RQM) Once you have identified the equal angles, you now apply the side ratio relationship. You must choose side opposite to corresponding angles. (1) gives you PQ/RQ (2) gives you QR/RM (3) gives you PM/QR. So, PQ/RQ=QR/RM=PM/QR. Here you do not need to first ratio. So, QR/RM=PM/QR => PM*RM=QR^2. This relationship in split right triangles is so favorite among GMAT, GRE, SAT, CAT, MBA tentmakers that you can memorize it.