In APQR, mZQ = 90, PQ = 3 cm,
PR = 6 cm, find ZQPR and ZPRQ.
P
6cm
6
3
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R
Answers
Answer:
Solution :
Analysis :
The length of three sides of △PQR are known
∴△PQR can be constructed.
△PQR~△PMN such that PRPN=53
∴ sides of trianglePMN are smaller than the corresponding sides of △PQRand∠QRP≅∠MPN ...(Corresponding angles of similar triangles)
∴△PQRand△PMN can have common angle P.
Consider the given analytical figure
If we divide Pr into 5 equal parts, then PN would be equal to three equal parts. Thus point N can be located on seg PR.
As, ∠PRQ≅∠PNM ...(Corresponding angles of similar triangles)
∴ at point N, we draw line NM || side QR intersectiong side PQ at M. Thus we obtain △PMN
Stepas of construction :
(1) Construct △PQR such that PQ = 4 cm , PR = 6 cm and QR = 5 cm
(2) Divide segment PR in 5 equal parts
Name the endpoint of the third part as N.
(4) Now, draw a line parallel to QR through N. Mark the point of intersection of the parallel line with PQ as M.
(5) △PMN is required triangle similar to △PQR
construction :