In the figure- - PQS- PRT and QS-TR- then - PQS- PRT by congruence postulate

The correct option is D AASIn PQS and PRT ⇒ #160; ∠ QPS=∠ RPT #160; #160; #160; #160; #160; #160; #160;[ Common an ...

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Byju's Answer

Standard VII

Mathematics

Properties of Isosceles and Equilateral Triangles

In the figure...

Question

In the figure, $∠ P Q S = ∠ P R T$ and QS=TR. then $Δ P Q S ≅ Δ P R T$ by congruence postulate

SAS

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SSS

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RHS

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AAS

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Solution

The correct option is D AAS
In $△ P Q S$ and $△ P R T$

$\Rightarrow$ $∠ Q P S = ∠ R P T$ [ Common angle ]

$\Rightarrow$ $∠ P Q S = ∠ P R T$ [ Given ]

$\Rightarrow$ $Q S = T R$ [ Given ]

$∴$ $△ P Q S ≅ △ P R T$ [ By $A A S$ congruence rule ]

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Similar questions

Q. In the figure, seg QS

⊥

side PR, seg RT

⊥

side PQ, P-S-R, and P-T-Q. Show that (i)

Δ P Q S \sim Δ P R T

Q. The given figure shows

P Q = P R

and

∠ Q = ∠ R

Prove that

Δ P Q S \equiv Δ P R T

Q. In the figure,

\frac{Q R}{Q S} = \frac{Q T}{P R} a n d

∠ 1 = ∠ 2

S h o w t h a t Δ P Q S \sim Δ T Q R

In the given figure, T is a point on side QR of $Δ P Q R$ and S is a point such that RT = ST.
Which of the following is true?

Question 87

In the given figure, area of $Δ P Q R$ is $20 c m^{2}$ and area of $Δ P Q S$ is $44 c m^{2}$ . Find the length RS, if PQ is perpendicular to QS and QR is 5 cm.

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In the figure, ∠PQS=∠PRT and QS=TR. then ΔPQS≅ΔPRT by congruence postulate

The correct option is D AASIn △PQS and △PRT⇒ ∠QPS=∠RPT [ Common angle ]⇒ ∠PQS=∠PRT [ Given ]⇒ QS=TR [ Given ]∴ △PQS≅△PRT [ By AAS congruence rule ]

In the figure, $∠ P Q S = ∠ P R T$ and QS=TR. then $Δ P Q S ≅ Δ P R T$ by congruence postulate

The correct option is D AAS
In $△ P Q S$ and $△ P R T$

$\Rightarrow$ $∠ Q P S = ∠ R P T$ [ Common angle ]

$\Rightarrow$ $∠ P Q S = ∠ P R T$ [ Given ]

$\Rightarrow$ $Q S = T R$ [ Given ]

$∴$ $△ P Q S ≅ △ P R T$ [ By $A A S$ congruence rule ]