Question

if in two triangles, corresponding angles are equal , then their corresponding sides are in the same ratio and hence the two angles are similar

Answer 1

THEOREM 3:

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. This is also called AAA (Angle-Angle-Angle) criterion.



Construction: Two triangles ABC and DEF are drawn so that their corresponding angles are equal. This means:

∠ A =∠ D, ∠ B = ∠ E and ∠ C = ∠ F

To prove:

ABDE=ACDF=BCEFABDE=ACDF=BCEF

Draw a line PQ in the second triangle so that DP = AB and PQ = AC

Proof:

ΔABC≅ΔDPQΔABC≅ΔDPQ

Because corresponding sides of these two triangles are equal

This means; ∠ B = ∠ P = ∠ E and PQ || EF

This means;

DPPE=DQQFDPPE=DQQF

Hence;

ABDE=ACDFABDE=ACDF

ABDE=BCEFABDE=BCEF

Hence;

ABDE=ACDF=BCEFABDE=ACDF=BCEF 



hence proved.... type JAI HIND...

Answer 2

Answer:

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