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Question

(a) In the given figure, prove that:



(i) PQ = RS

(ii) PS = QR


(b) Which congruence criterion will you use in the following?

(i) Given: ∠ MLN = ∠ FGH

∠ NML = ∠ GFH

ML = FG

So, ΔLMN ≅ ΔGFH

(ii) Given: EB = DB

AE = BC

∠ A = ∠ C = 90°

So, ΔABE ≅ ΔCDB
.
​​​​​​​[4 MARKS]

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Solution

Each part: 2 Marks

(a) In ΔPSR and ΔRQP

PSR=RQP [Given]

SPR=QRP [Given]

PR=PR [Common]

ΔPSRΔRQP [AAS congruency criteria]

(i) PQ=RS [Corresponding parts of congruent triangles]

(ii) Also, PS=QR [Corresponding parts of congruent triangles]


(b) (i) ASA, as two angles and the side included between these angles of ΔLMN, are equal to two angles and the side included between these angles of ΔGFH.

(ii) RHS, as in the given two right-angled triangles, one side and the hypotenuse are respectively equal.


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