178

You visited us 178 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VI

Mathematics

Angle

In the given ...

Question

In the given figure, $A B = B C$ and $A C = C D$ . Prove that: $∠ B A D : ∠ A D B = 3 : 1$ .

Open in App

Solution

Let $∠ A D B = x$

In $△ A C D, A C = C D$

$\Rightarrow ∠ C A D = ∠ C D A = x$

and, $∠ A C B = ∠ C A D + ∠ C D A = x + x = 2 x$

$\Rightarrow ∠ B A C = ∠ A C B = 2 x . (∵$ In $A B C, A B = B C)$

$∴ ∠ B A D = ∠ B A C + ∠ C A D$

$= 2 x + x = 3 x$

And, $\frac{∠ B A D}{∠ A D B} = \frac{3 x}{x} = \frac{3}{1}$

i.e., $∠ B A D : ∠ A D B = 3 : 1$ $[h e n c e p r o v e d]$

Suggest Corrections

Similar questions

In the given figure, AB = BC and AC = CD. Find the ratio of ∠BAD: ∠ADB.

Q. In the following figure:

A C = C D; ∠ B A D = 110^{o}

and

∠ A C B = 74^{o}

.
Prove that:

B C > C D

$In the given figure, prove that (i) CD + DA + AB > B C (ii) CD + DA + AB + BC > 2 A C .$

In the adjoining figure, $A B = A C$ and $B D = D C$ . Prove that $Δ A D B ≅ Δ A D C$ and hence show that
$(i) ∠ A D B = ∠ A D C = 90^{\circ}$
$(i i) ∠ B A D = ∠ C A D$

Q. Question 3
ABC is an isosceles triangle with AB = AC and D is a point on BC such that

A D ⊥ B C

(see figure). To prove that

∠ B A D = ∠ C A D

, a student proceeded as follows.

Δ A B D

and

Δ A C D

, we have AB= AC [given]

∠ B = ∠ C

[because AB=AC]
And

∠ A D B = ∠ A D C

Therefore,

Δ A B D ≅ Δ A C D

[by AAS congruence rule]
So,

∠ B A D = ∠ C A D

[by CPCT]
What is the defect in the above arguments?

Join BYJU'S Learning Program

In the given figure, AB=BC and AC=CD. Prove that: ∠BAD:∠ADB=3:1.

Let ∠ADB=xIn △ACD,AC=CD⇒∠CAD=∠CDA=xand, ∠ACB=∠CAD+∠CDA=x+x=2x⇒∠BAC=∠ACB=2x.(∵ In ABC,AB=BC)∴∠BAD=∠BAC+∠CAD=2x+x=3xAnd, ∠BAD∠ADB=3xx=31i.e., ∠BAD:∠ADB=3:1 [henceproved]

In the given figure, $A B = B C$ and $A C = C D$ . Prove that: $∠ B A D : ∠ A D B = 3 : 1$ .