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Standard VII

Mathematics

Exterior Angle of a Triangle and Its Property

Question 144 ...

Question

Question 144 (ii)

ABC is an isosceles triangle with AB = AC and D is the mid-point of base BC (see the figure)

Is $Δ A B D ≅ Δ A C D$ ? If so why?

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Solution

Given, AB = AC and BD = CD

Also, AD = AD
Hence, $Δ A B D ≅ Δ A C D$ by SSS congruence criterion.

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Similar questions

Question 144 (i)

ABC is an isosceles triangle with AB = AC and D is the mid-point of base BC (see the figure)
State three pairs of equal parts in the $Δ A B D$ and $Δ A C D$

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?

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?

Q. ABC is an isosceles triangle with AB

=

AC and D is a point on BC such that

A D ⊥ B C

(Fig. 7.13). To prove that

∠ B A D = ∠ C A D,

a student proceeded as follows:

Δ A B D

and

Δ A C D,

=

AC (Given)

∠ B = ∠ C

(because AB

=

AC)
and

∠ A D B = ∠ A D C

Therefore,

Δ A B D ≅ Δ A C D (A A S)

So,

∠ B A D = ∠ C A D (C P C T)

What is the defect in the above arguments?

Question 11
In the following figure, E is a point on side CB produced, of an isosceles triangle ABC, with AB = AC. If AD $⊥$ BC and EF $⊥$ AC, prove that $Δ A B D \sim Δ E C F$ .

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Question 144 (ii) ABC is an isosceles triangle with AB = AC and D is the mid-point of base BC (see the figure) Is ΔABD≅ΔACD? If so why?

Given, AB = AC and BD = CD Also, AD = AD Hence, ΔABD≅ΔACD by SSS congruence criterion.

Question 144 (ii)

ABC is an isosceles triangle with AB = AC and D is the mid-point of base BC (see the figure)

Is $Δ A B D ≅ Δ A C D$ ? If so why?

Given, AB = AC and BD = CD

Also, AD = AD
Hence, $Δ A B D ≅ Δ A C D$ by SSS congruence criterion.