Q133 of 158 Page 159

In Fig. 6.41, ∆PQR is right-angled at P. U and T are the points on line QRF. If QP || ST and US || RP, find ∠S.


Given: QP || ST ; US || RP; ∠P = 90°


Formula Used/Theory:-


If all sides of both the triangles are parallel than then they are similar triangles


And their angles will also be equal


In Δ PQR and Δ STU


PQ || ST (given)


PR ||SU (given)


QR || TU (both lies on same line)


∴ Δ PQR ~ Δ STU


Then;


∠P = ∠S; ∠Q = ∠T; ∠R = ∠U


If ∠P = 90°


Then; ∠S = 90°


Result:- angle S measured out to be 90°


More from this chapter

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 132

In Δ DEF, ∠D = 60°, ∠E = 70° and the bisectors of ∠E and ∠F meet at O. Find

(i) ∠F


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 134

In each of the given pairs of triangles of Fig. 6.42, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.



 135

In each of the given pairs of triangles of Fig. 6.43, using only RHS congruence criterion, determine which pairs of triangles are congruent. In case of congruence, write the result in symbolic form: