Criteria for Similarity of Triangles

Is the following pair of triangles similar? If so, find the similarity postulate used.

Is the following pair of triangles similar? If so, find the similarity postulate used.

Is the following pair of triangles similar? If so, find the similarity postulate used.

Is the following pair of triangles similar? If so, find the similarity postulate used.

Write down the similarity postulate that proves the triangles are similar. Then find the missing measurement. Round your answers to 3 s.f.

Write down the similarity postulate that proves the triangles are similar. Then find the missing measurement. Round your answers to 3 s.f.

Prove that the line segment joining the midpoints of the sides of a triangle from four triangles, each of which is similar to the original triangle.

$\mathrm{CM} \& \mathrm{RN}$ are respectively the medians of similar triangles $△\mathrm{ABC}$ and $△\mathrm{PQR}$. Prove that $△\mathrm{CMB}~△\mathrm{RNQ}$ .

$\mathrm{CM} \& \mathrm{RN}$ are respectively the medians of similar triangles $△\mathrm{ABC}$ and $△\mathrm{PQR}$. Prove that $△\mathrm{AMC}~△\mathrm{PNR}$.

Are triangles formed in figure similar? If so, name the criterion of similarity. Write the similarity relation in symbolic form.

Are triangles formed in a figure similar? If so, name the criterion of similarity. Write the similarity relation in symbolic form.

In $△ACB, \angle C=90°$ and $CD\perp AB$. Prove that $\frac{B{C}^2}{A{C}^2}=\frac{BD}{AD}$.

Is the pair of polygons given below similar or not similar? Why? 

Check for similarity in the triangles and explain which criterion is used.

$\text{△OAB}$ and $\text{△OKT}$

In the given figure, $\angle PQR = \angle PST = 90°, PQ = 5 \mathrm{cm}$ and $PS = 2 \mathrm{cm}$. Prove that $△PQR ~ △PST$.

$\mathrm{O}$ is the point of intersection of the diagonals $\mathrm{AC}$ and $\mathrm{BD}$ of a trapezium $\mathrm{ABCD}$ with $\mathrm{AB}\parallel \mathrm{DC}$. Through $\mathrm{O}$, a line segment $\mathrm{PQ}$ is drawn parallel to $\mathrm{AB}$ meeting $\mathrm{AD}$ in$\mathrm{P}$ and $\mathrm{BC}$ in $\mathrm{Q}$, then $\mathrm{OP}$ is equal to

$P$ and $Q$ are the points on sides $AB$ and $AC$, respectively of $△ABC$. If $AP=3 \mathrm{cm}$, $PB= 6 \mathrm{cm}, AQ= 5 \mathrm{cm}$and $QC=10 \mathrm{cm}$, show that $BC=3PQ$.

In the given figure, if $\angle BAC=90°$ and $AD\perp BC$, prove that $A{D}^2=BD.CD$.

A boy of height $90 \mathrm{cm}$ is walking away from the base of a lamp-post at a speed of $1.2 \mathrm{m}/\mathrm{s}$. If the lamp is $3.6 \mathrm{m}$ above the ground, then the length of his shadow after $6 \mathrm{s}$ is

In the given figure, $ABC$ is a right-angled triangle with $\angle BAC=90°$. $AD$ is the perpendicular drawn on side $BC$ dividing it into two parts. $CD$ is $8 cm$ and $BD$ is $18 cm$. Prove that $△ADB~△CDA$.