Q18 of 62 Page 193

Δ ABC is a right angled triangle where ∠B = 90° and BD ⊥ AC. If BD = 8 cm, AD = 4 cm, then CD is


In ΔABC and ΔADB,


∠ A = ∠ A {Common}


∠ B = ∠ D {90° each}


By the criterion of similar triangle AA which says that


if two angles of one triangle are respectively equal to two angles of another triangle then the two triangles are similar


ΔABC ~ ΔADB …(1)


In ΔABC and ΔBDC,


∠ C = ∠ C {Common}


∠ B = ∠ D {90° each}


By the criterion of similar triangle AA which says that


if two angles of one triangle are respectively equal to two angles of another triangle then the two triangles are similar


ΔABC ~ ΔBDC …..(2)


From (1) and (2),


ΔBDC ~ ΔADB



Putting the values,



⇒ CD = 16 cm

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