Question

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

Answer 1

Steps of construction:

1. Draw seg AT of length 4.9 cm
2. Take ∠A as 120° and draw an arc of 6.3 cm on it. Name the point as M.
3. Join seg MT to obtain ΔAMT.
4. Draw ray AB such that ∠TAB is an acute angle.
5. Locate points B₁, B₂, B₃, B₄, B₅, B₆, B₇ on ray AB such that,
   AB₁ = B₁B₂ = B₂B₃ = B₃B₄ = B₄B₅ = B₅B₆ = B₆B₇.
6. Join point T and B₇.
7. Through point, B₅ draw a line parallel to seg TB₇ which intersects seg AT at point E.
8. Draw a line parallel to MT through E to intersect line AM at point H.
   ∆AHE is the required triangle similar to ∆AMT.