If figure OPRQ is a square and &ang;MLN = 90°. Prove that ∆QMO ~ ∆RPN

In ∆QMO and ∆RPN &ang;MQO = &ang;NRP = 90° &ang;RPN = &ang;QOM ...(OP || MN) &there4; ∆QMO ~ ∆RPN ...(By AA similarity)

If figure OPRQ is a square and ∠MLN = 90°. Prove that ∆QMO ~ ∆RPN - Mathematics

If figure OPRQ is a square and ∠MLN = 90°. Prove that ∆QMO ~ ∆RPN

Sum

In ∆QMO and ∆RPN

∠MQO = ∠NRP = 90°

∠RPN = ∠QOM ...(OP || MN)

∴ ∆QMO ~ ∆RPN ...(By AA similarity)

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Chapter 4: Geometry - Exercise 4.1 [Page 171]

Chapter 4 Geometry
Exercise 4.1 | Q 7. (iii) | Page 171

Area of two similar triangles are 98 sq. cm and 128 sq. cm. Find the ratio between the lengths of their corresponding sides.

ΔABC ~ ΔDEF and their areas are respectively `100cm^2` and `49cm2`. If the altitude of ΔABC is 5cm, find the corresponding altitude of ΔDEF.

Are the triangles in the given figure similar? If yes, by which test?

Δ ABC ∼ Δ PQR such that AB= 1.5 cm and PQ=2. 1 cm. Find the ratio of areas of Δ ABC and ΔPQR.

The scale of a map is 1 : 200000. A plot of land of area 20km² is to be represented on the map. Find:

The number of kilometres on the ground represented by lcm or the map

On a map drawn to a scale of 1 : 2,50,000; a triangular plot of land has the following measurements : AB = 3 cm, BC = 4 cm and angle ABC = 90°.

Calculate : the area of the plot in sq. km.

In ΔABC, point D divides AB in the ratio 5:7, Find: `"AD"/"AB"`

In the figure, PQR is a straight line and PS || RT. If QS = 12cm, QR = 15cm, QT = 10cm and RT = 6cm, find PQ and PS.

ΔABC has been reduced by a scale factor 0.6 to ΔA'B'C'/ Calculate:Length of B' C', if BC = 8cm

∆ABC ~ ∆PQR. If AM and PN are altitudes of ΔABC and ∆PQR respectively and AB² : PQ² = 4 : 9, then AM : PN = ______.