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Diagram

ΔAMT ~ ΔAHE. In ΔAMT, AM = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `"AM"/"HA" = 7/5`, then construct ΔAMT and ΔAHE

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#### Solution

**Steps of construction:**

- Draw seg AT of length 4.9 cm
- Take ∠A as 120° and draw an arc of 6.3 cm on it. Name the point as M.
- Join seg MT to obtain ΔAMT.
- Draw ray AB such that ∠TAB is an acute angle.
- Locate points B
_{1}, B_{2}, B_{3}, B_{4}, B_{5}, B_{6}, B_{7}on ray AB such that,

AB_{1}= B_{1}B_{2}= B_{2}B_{3}= B_{3}B_{4}= B_{4}B_{5}= B_{5}B_{6}= B_{6}B_{7}. - Join point T and B
_{7}. - Through point, B
_{5}draw a line parallel to seg TB_{7}which intersects seg AT at point E. - Draw a line parallel to MT through E to intersect line AM at point H.

∆AHE is the required triangle similar to ∆AMT.

Concept: Division of a Line Segment

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