The line segment joining the mid-points of any two sides of a triangle is parallel to the third side.
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In the given pairs of triangles, find which pair of triangles are similar. State the similarity criterior and write the similarity relation in symbolic from.
ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that $\text{CQ}=\frac{1}{4}\text{AC}.$ If PQ produced meets BC at R, prove that R is the midpoint of BC.
In the given pairs of triangles, find which pair of triangles are similar. State the similarity criterior and write the similarity relation in symbolic from.
In the given figure, $\angle\text{CAB}=90^\circ$ and $\text{AD}\perp\text{BC}.$ Show that $\triangle\text{BDA}\sim\triangle\text{BAC}.$ If AC = 75cm, AB = 1m, and BC = 1,25m find AD.
In the given figure, O is a point inside a $\triangle\text{PQR}$ such that $\angle\text{PQR}=90^\circ,\text{OP}=6\text{cm}$ and $\text{OR}=8\text{cm}.$ If $\text{PQ}=24\text{cm}$ and $\text{QR}=26\text{cm},$ prove that $\triangle\text{PQR}$ is right-angled.