Q6 of 70 Page 140

Fill in the blanks so that the following statements are true:

In ΔABC, and are altitudes. If AB = 12, BC = 15 and AM = 9.6, then CN = _____.

We have



Given: AM ⊥ BC and CN ⊥ AB.


AB = 12, BC = 15 & AM = 9.6


To find: CN = ?


For this,


Take ∆AMB and ∆CNB,


∠AMB = ∠CNB [∵, ∠AMB = ∠CNB = 90°]


∠ABM = ∠CBN [∵, ∠AMB and ∠CBN are same angles of the same triangle ABC]


⇒ By AA corollary, ∆AMB ∼ ∆CNB for the correspondence AMB ↔ CNB.


By definition, for a given correspondence between the vertices of two triangles, if the corresponding angles of the triangles are congruent and the lengths of the corresponding sides are in proportion, then the given correspondence is a similarity between two triangles.


⇒


Or


⇒


⇒


⇒


⇒ CN = 12


Thus, answer is 12.


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