Question

In the given figure,
$AB \parallel DC$ prove that
(i) $\triangle DMU \sim \triangle BMV$
(ii) DM × BV = BM ✕ DU

Answer 1

Answer:

It is proved that DM × BV = BM × DU  

Step-by-step explanation:

Given :

AB || DC

(i) In ∆ DMU & ∆ BMV  

∠MDU = ∠MBV  (alternate interior angles)

∠DMU = ∠BMV  (vertically opposite angles)

∆ DMU ~ ∆BMV   [By AA similarity criterion]]

(ii) DM/BM = DU/BV  

[Corresponding sides of similar triangles are proportional]

By cross multiplication,  

DM × BV = BM × DU  

Hence,proved that DM × BV = BM × DU  

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