Question

Explain, why
ΔABC ≅ ΔFED

Solution

Given that, ∠ABC = ∠FED (1)

∠BAC = ∠EFD (2)

The two angles of ΔABC are equal to the two respective angles of ΔFED. Also, the sum of all interior angles of a triangle is 180º. Therefore, third angle of both triangles will also be equal in measure.

∠BCA = ∠EDF (3)

Also, given that, BC = ED (4)

By using equation (1), (3), and (4), we obtain

ΔABC ≅ ΔFED (ASA criterion)

Some More Questions From Congruence of Triangles Chapter

You want to show that ΔART ≅ ΔPEN,
(a) If you have to use SSS criterion, then you need to show
(i) AR = (ii) RT = (iii) AT =
(b) If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have
(i) RT = and (ii) PN =
(c) If it is given that AT = PN and you are to use ASA criterion, you need to have
(i) ? (ii) ?

You have to show that ΔAMP ≅ AMQ.
In the following proof, supply the missing reasons.

–

Steps

–

Reasons

(i)

PM = QM

(i)

…

(ii)

∠PMA = ∠QMA

(ii)

…

(iii)

AM = AM

(iii)

…

(iv)

ΔAMP ≅ ΔAMQ

(iv)

…

In ΔABC, ∠A = 30°, ∠B = 40° and ∠C = 110°
In ΔPQR, ∠P = 30°, ∠Q = 40° and ∠R = 110°
A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or why not?

In a squared sheet, draw two triangles of equal areas such that
(i) The triangles are congruent.
(ii) The triangles are not congruent.
What can you say about their perimeters?

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Congruence Of Triangles

Explain, why
ΔABC ≅ ΔFED

Some More Questions From Congruence of Triangles Chapter

You have to show that ΔAMP ≅ AMQ.
In the following proof, supply the missing reasons.

–

Steps

–

Reasons

(i)

PM = QM

(i)

…

(ii)

∠PMA = ∠QMA

(ii)

…

(iii)

AM = AM

(iii)

…

(iv)

ΔAMP ≅ ΔAMQ

(iv)

…

In ΔABC, ∠A = 30°, ∠B = 40° and ∠C = 110°
In ΔPQR, ∠P = 30°, ∠Q = 40° and ∠R = 110°
A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or why not?

In a squared sheet, draw two triangles of equal areas such that
(i) The triangles are congruent.
(ii) The triangles are not congruent.
What can you say about their perimeters?

Explain, why
ΔABC ≅ ΔFED

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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–	Steps	–	Reasons
(i)	PM = QM	(i)	…
(ii)	∠PMA = ∠QMA	(ii)	…
(iii)	AM = AM	(iii)	…
(iv)	ΔAMP ≅ ΔAMQ	(iv)	…

For Daily Free Study Material Join wiredfaculty

Congruence Of Triangles

Explain, whyΔABC ≅ ΔFED

Some More Questions From Congruence of Triangles Chapter

You have to show that ΔAMP ≅ AMQ.In the following proof, supply the missing reasons. – Steps – Reasons (i) PM = QM (i) … (ii) ∠PMA = ∠QMA (ii) … (iii) AM = AM (iii) … (iv) ΔAMP ≅ ΔAMQ (iv) …

In ΔABC, ∠A = 30°, ∠B = 40° and ∠C = 110°In ΔPQR, ∠P = 30°, ∠Q = 40° and ∠R = 110°A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or why not?

In a squared sheet, draw two triangles of equal areas such that(i) The triangles are congruent.(ii) The triangles are not congruent.What can you say about their perimeters?

Explain, whyΔABC ≅ ΔFED

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Explain, why
ΔABC ≅ ΔFED

You have to show that ΔAMP ≅ AMQ.
In the following proof, supply the missing reasons.

–

Steps

–

Reasons

(i)

PM = QM

(i)

…

(ii)

∠PMA = ∠QMA

(ii)

…

(iii)

AM = AM

(iii)

…

(iv)

ΔAMP ≅ ΔAMQ

(iv)

…

In ΔABC, ∠A = 30°, ∠B = 40° and ∠C = 110°
In ΔPQR, ∠P = 30°, ∠Q = 40° and ∠R = 110°
A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or why not?

In a squared sheet, draw two triangles of equal areas such that
(i) The triangles are congruent.
(ii) The triangles are not congruent.
What can you say about their perimeters?

Explain, why
ΔABC ≅ ΔFED