In - ABC-AB-AC and AD BC- Then the line of symmetry is

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Standard VIII

Mathematics

Observing Congruency Using Reflection

In Δ ABC,AB...

Question

In $Δ A B C, A B = A C$ and $A D ⊥ B C$ . Then the line of symmetry is

A B

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A C

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B D

and

D C

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A D

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Solution

The correct option is D $A D$
$Δ A B D ≅ Δ A D C,$
Hence, $B D = D C$ , A coincides with A,
$A B = A C, a n d ∠ B A D = ∠ C A D$ . Therefore, B coincides with C.
Hence, AD is the line of symmetry of $Δ A B C$ .

Suggest Corrections

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A C

In a $Δ A B C$ , AD is the bisector of $∠ A$ , meeting side BC at D.
(i) If BD= 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD= 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB= 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB =10 cm, AC =14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.
(vi) If AD= 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AB= 3.6 cm, BC e 6 cm and BD = 32 cm, find AC.
(viii) If AB =10 cm, AC = 6 cm and BC = 12 cm, find BD and DC