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GradeSimilarity of Triangles, Similarity of Triangles

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\[\vartriangle ABC\] is similar to \[\vartriangle PQR\]. \[AB\] corresponds to \[PQ\] and \[BC\] corresponds to \[QR\]. If \[AB = 9\], \[BC = 12\], \[CA = 6\] and \[PQ = 3\], what are the lengths of \[QR\] and \[RP\]?

A vertical stick \[20{\text{ m}}\] long casts a shadow \[10{\text{ m}}\] long on the ground, at the same time a tower casts a shadow \[50{\text{ m}}\] long on the ground, the height of the tower is?

A) \[100{\text{ m}}\]

B) \[120{\text{ m}}\]

C) \[25{\text{ m}}\]

D) \[200{\text{ m}}\]

A) \[100{\text{ m}}\]

B) \[120{\text{ m}}\]

C) \[25{\text{ m}}\]

D) \[200{\text{ m}}\]

Given, \[D\] is the midpoint of side \[BC\] of a \[\vartriangle ABC\] . \[AD\] is bisected at the point \[E\] and \[BE\] produces cuts \[AC\] at the point \[X\] . Prove that \[BE:EX = 3:1\] .

In the given figure,find the value of \[x\] in terms of \[a\],\[b\] and \[c\].

In a $ \vartriangle PQR $ , $ P{R^2} - P{Q^2} = Q{R^2} $ and $ M $ is a point on side $ PR $ such that $ QM \bot PR $ , prove that $ Q{M^2} = PM \times MR $ .

In given figure , if DE|| BC, then the value of x is equal to

(A). 3 cm

(B). 4 cm

(C). 7 cm

(D). 4.7 cm

(A). 3 cm

(B). 4 cm

(C). 7 cm

(D). 4.7 cm

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Given $area\left( \Delta ABC \right)=360c{{m}^{2}},area\left( BPQC \right)=110c{{m}^{2}}$, $PQ||BC;AP=10cm$. Find $\dfrac{AQ}{QC}$.

If two triangles $\Delta DEF\sim \Delta PQR$. If 2DE = 3PQ, QR = 8 and DF = 6 then find EF and PR?

If similar triangles, $\Delta ABC\sim \Delta DEF$ in which $AH$ and $DY$ are the bisectors of $\angle A$ and $\angle D$ respectively. If $AH=6.5\,\text{ cm}$ and $DY=5.2\text{ cm}$ , find the ratio of the area of $\Delta ABC$ and $\Delta DEF$ .

In the figure $\angle M=\angle N={{46}^{\circ }}$, express $x$ in terms of a, b and c where lengths of LM, MN and NK are a, b, c respectively. $PN=x$.

In quadrilateral \[ACBD\],

\[AC = AD\] and \[AB\]bisects \[\left| \!{\underline {\,

A \,}} \right. \]. Show that \[\Delta \;ABC \cong \Delta \;ABD\]. What can you say about \[BC\]and \[BD\] \[?\]

\[AC = AD\] and \[AB\]bisects \[\left| \!{\underline {\,

A \,}} \right. \]. Show that \[\Delta \;ABC \cong \Delta \;ABD\]. What can you say about \[BC\]and \[BD\] \[?\]

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