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Standard IX

Mathematics

Congruent Triangles

In Δ ABD, AB ...

Question

In $Δ A B D$ , AB = AD and AC is perpendicular to BD. State the congruence rule by which $Δ A C B ≅ Δ A C D$ .

SAS congruence rule

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SSS congruence rule

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RHS congruence rule

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ASA congruence rule

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Solution

The correct option is C
RHS congruence rule

$In the given triangle, A B = A D (Given) A C is the common side ∠ A C B = ∠ A C D = 90^{\circ}$

$∴ Δ A C B ≅ Δ A C D$ [ RHS criteria]

Hence, by RHS congruence rule, the two triangles are congruent.

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Similar questions

In $Δ A B D$ , AB = AD and AC is perpendicular to BD. State the congruence rule by which $Δ A C B ≅ Δ A C D$ .

In $Δ$ ABD, AB=AD and AC is perpendicular to BD. State the property by which $Δ$ ACB $≅$ $Δ$ ACD.

Q. Given:

Δ A ⊥ A B

C B ⊥ A B

and

A C = B D

State

3

points of equal pairs in

Δ A B C

Δ A B D

& Congruence rule.

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?

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In ΔABD, AB = AD and AC is perpendicular to BD. State the congruence rule by which ΔACB≅ΔACD.

The correct option is C RHS congruence rule In the given triangle,AB=AD(Given)AC is the common side∠ACB=∠ACD=90∘ ∴ΔACB≅ΔACD [ RHS criteria] Hence, by RHS congruence rule, the two triangles are congruent.

In $Δ A B D$ , AB = AD and AC is perpendicular to BD. State the congruence rule by which $Δ A C B ≅ Δ A C D$ .

The correct option is C
RHS congruence rule

$In the given triangle, A B = A D (Given) A C is the common side ∠ A C B = ∠ A C D = 90^{\circ}$

$∴ Δ A C B ≅ Δ A C D$ [ RHS criteria]

Hence, by RHS congruence rule, the two triangles are congruent.