In , point is taken on and point on . The measured lengths are: , , , and…

MATHEMATICS · Multi-part · US High School · Geometry · Similarity · Similarity

Problem

\triangle XYZ

, point

A

is taken on

XY

and point

B

XZ

. The measured lengths are:

XA = 3.6\,\text{cm}

AY = 5.4\,\text{cm}

XB = 4.8\,\text{cm}

, and

BZ = 7.2\,\text{cm}

. (i) Determine whether

A

and

B

divide the respective sides in the same ratio. (ii) What can you conclude about the position of

AB

with respect to

YZ

? (iii) Give a clear reason for your conclusion in part (ii).