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Standard VII

Mathematics

SAS Criteria for Congruency

i State which...

Question

Question 149 (i)

State which of the following pairs of triangles are congruent. If yes, write them in symbolic form (you may draw a rough figure).

$Δ P Q R : P Q = 3.5 c m,$ $Q R = 4.0 c m$ , $∠ Q = 60^{\circ}$
$Δ S T U : S T = 3.5 c m$ , $T U = 4.0 c m$ , $∠ T = 60^{\circ}$

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Solution

Both the triangles are congruent.
$∴$ $Δ P Q R ≅ Δ S T U$ [by SAS congruence criterion]

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Similar questions

Question 149 (ii)

State whether the given pair of triangles is congruent. If yes, write them in symbolic form (you may draw a rough figure).

$Δ A B C : A B = 4.8 c m$ $∠ A = 90^{\circ}$ , $A C = 6.8 c m$
$Δ X Y Z : Y Z = 6.8 c m$ , $∠ X = 90^{\circ}$ , $Z X = 4.8 c m$

State which pairs of triangles in the following figure are similar? Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Q. In

△ A B C

and

△ P Q R

, if

A B = 2.5 c m, A C = 3.5 c m, B C = 4.0 c m, P Q = 5 c m, P R = 7 c m

and

Q R = 8 c m

, then find whether

△ A B C

and

△ P Q R

are similar or not

Q. State which pair of triangles in figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form:

Q. Construct a quadrilateral ABCD with AB = 3.5 cm, BC = 4.0 cm, CD = 5.0 cm, DA = 4.0 cm and

∠ B = 45^{\circ}

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Question 149 (i) State which of the following pairs of triangles are congruent. If yes, write them in symbolic form (you may draw a rough figure). ΔPQR:PQ=3.5 cm, QR=4.0 cm, ∠Q=60∘ ΔSTU:ST=3.5 cm, TU=4.0 cm, ∠T=60∘

Both the triangles are congruent. ∴ ΔPQR≅ΔSTU [by SAS congruence criterion]

Question 149 (i)

State which of the following pairs of triangles are congruent. If yes, write them in symbolic form (you may draw a rough figure).

$Δ P Q R : P Q = 3.5 c m,$ $Q R = 4.0 c m$ , $∠ Q = 60^{\circ}$
$Δ S T U : S T = 3.5 c m$ , $T U = 4.0 c m$ , $∠ T = 60^{\circ}$

Both the triangles are congruent.
$∴$ $Δ P Q R ≅ Δ S T U$ [by SAS congruence criterion]