Question

"If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar."

PROVE THE ABOVE THEOREM....NEED URGENTLY....NO SPAM | COPY/PASTE​

Answer 1

Step-by-step explanation:

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

theorem on similarity of triangles

Construction: ABC is a triangle. DE || BC and DE intersects AB at D and AC at E.

Join B to E and C to D. Draw DN ⊥ AB and EM ⊥ AC.

To prove:theorem on similarity of triangles

Proof:

ar (AEM)theorem on similarity of triangles

Similarly;

theorem on similarity of triangles

Hence;

theorem on similarity of triangles

Similarly;

theorem on similarity of triangles

Triangles BDE and DEC are on the same base, i.e. DE and between same parallels, i.e. DE and BC.

Hence, ar(BDE) = ar(DEC)

From above equations, it is clear that;

theorem on similarity of triangles

Answer 2

Answer:

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