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SAS Criteria for Congruency

Ankita wants ...

Question

Ankita wants to prove $Δ A B C ≅ Δ D E F$ using $S A S$ . She knows $A B = D E$ and $A C = D F$ . What additional piece of information does she need?

∠ A = ∠ D

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∠ C = ∠ F

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∠ B = ∠ E

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∠ A = ∠ B

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Solution

The correct option is A $∠ A = ∠ D$
By SAS, two corresponding sides and their included angles should be congruent.
Since $A B = D E$ and $A C = D F$ ,
The included angles of $A B$ and $A C = ∠ A$
and included angle of $D E$ and $D F = ∠ D .$
$\Rightarrow ∠ A = ∠ D$ is needed.

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Similar questions

Q. To prove that

Δ D E F

and

Δ A B C

are congruent by SAS, what additional information is needed?

In ∆ABC and ∆DEF, AB = DF and ∠A = ∠D. The two triangles will be congruent by SAS axiom if:

Q. Question 11 (v)
In

Δ A B C a n d Δ D E F

,AB=DE, AB || DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that AC = DF .

Q. in

Δ A B C

and

Δ D E F

A B = D E, A B | | D E, B C = E F

and

B C | | E F

. Vertices

A, B

and

C

are joined to vertices

D, E

and

F

respectively. Show that
(i) quadrilateral

A B E D

is parallelogram
(ii) quadrilateral

B E F C

is a parallelogram
(iii)

A D | | C F

and

A D = C F

(iv) quadrilateral

A C F D

is a parallelogram
(v)

A C = D F

(vi)

Δ A B C ≅ Δ D E F

In $Δ A B C a n d Δ D E F$ , AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B, and C are joined to vertices D, E and F respectively ( see the given figure).

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Ankita wants to prove ΔABC≅ΔDEF using SAS. She knows AB=DE and AC=DF. What additional piece of information does she need?

The correct option is A ∠A=∠DBy SAS, two corresponding sides and their included angles should be congruent. Since AB=DE and AC=DF,The included angles of AB and AC=∠A and included angle of DE and DF=∠D. ⇒∠A=∠D is needed.

Ankita wants to prove $Δ A B C ≅ Δ D E F$ using $S A S$ . She knows $A B = D E$ and $A C = D F$ . What additional piece of information does she need?

The correct option is A $∠ A = ∠ D$
By SAS, two corresponding sides and their included angles should be congruent.
Since $A B = D E$ and $A C = D F$ ,
The included angles of $A B$ and $A C = ∠ A$
and included angle of $D E$ and $D F = ∠ D .$
$\Rightarrow ∠ A = ∠ D$ is needed.