Question

two triangle ABC and DEF are equiangular then L and M are perpendicular from A and B on opposite side BC and EF respectively prove that BC/EF= AL/DM

Answer 1

Answer:

Step-by-step explanation:

Since ΔABC and ΔDEF are equiangular we can say that ∠L ≡ ∠M.

We want to prove that $\frac{BC}{EF}  = \frac{AL}{DM}$ .

There is a theorem that says that, in two triangles, if ∠Z and ∠F are congruent, then they have two congruent opposite sides.

Thus, since the triangle is equiangular, i.e, the angles are congruent, then we conclude, by the theorem that its sides are congruent too.

Then, we conclude that ΔABC and ΔDEF are congruent, i.e, ΔABC ≡ ΔDEF.

Thus, since sides and angles are congrent, and the triangle is congruent to we can say that:

$\frac{BC}{EF}  = \frac{AL}{DM}$

Hence, proven.