In the figure, M and N are the mid-points of PQ and PR respectively.

In the figure, M and N are the mid-points of PQ and PR respectively. QN and RM intersect at T.
(a) Prove that triangleTMN ~ triangleTRO.
(b) Find MT:TR.
 

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1 Answer

Angles of the same colour are congruent.

Triangles PMN and PQR are similar because PN/PR=PM/PQ=1/2 since M and N are midpoints, and angle QPR is common to both triangles. MN is parallel to QR, hence the blue angles and the green angles are congruent (opposite sides of the same transversal). The red angles are also congruent. MN/QR=1/2 because PMN and PQR are similar

(a) Therefore the triangles TMN and TRO are similar (coloured angles are congruent).

(b) Because triangles TMN and TRO are similar, MT/TR=MN/QR=1/2, or MT:TR=1:2.

by Top Rated User (1.1m points)

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