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GradeCriteria for Similarity of Triangles, Criteria for Similarity of Triangles

TopicLatest Questions

Triangle ABC is similar to triangle DEF.

Calculate the value of

a). \[x\],

b). \[y\]

Calculate the value of

a). \[x\],

b). \[y\]

A girl of height 90 cm is walking away from the base of a lamp-post at a speed at 1.2 m/sec. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.

ABCD is a rhombus and P, Q, R, S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

State \[AAA\] - similarity criteria ?

ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that

\[\dfrac{{ar\left( {ABC} \right)}}{{ar\left( {DBC} \right)}} = \dfrac{{AO}}{{DO}}\]

\[\dfrac{{ar\left( {ABC} \right)}}{{ar\left( {DBC} \right)}} = \dfrac{{AO}}{{DO}}\]

A man of height 1.8m is standing near a pyramid. If the shadow of the man is of length 2.7m and the shadow of the pyramid is 210m long at that instant, find the height of the pyramid.

D, E, F are respectively the mid points of the sides BC, CA and AB of a $\Delta ABC$. Show that

(i) BDEF is a parallelogram

(ii) $ar\left( \Delta DEF \right)=\dfrac{1}{4}ar\left( \Delta ABC \right)$

(iii) $ar\left( BDEF \right)=\dfrac{1}{2}ar\left( \Delta ABC \right)$

(i) BDEF is a parallelogram

(ii) $ar\left( \Delta DEF \right)=\dfrac{1}{4}ar\left( \Delta ABC \right)$

(iii) $ar\left( BDEF \right)=\dfrac{1}{2}ar\left( \Delta ABC \right)$

Diagonals AC and BD of a trapezium ABCD with $AB\parallel DC$ intersect each other at the point O . Using similarity criterion for two triangles, show that $\dfrac{OA}{OC}=\dfrac{OB}{OD}$.

State which pairs of triangles in figure are similar? Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form:

In the given figure \[E\] is a point on side \[CB\] produced of an isosceles triangle \[ABC\] with \[AB = AC\]. If \[AD \bot BC\] and \[EF \bot AC\] , prove that \[\Delta ABD \sim \Delta ECF\].

If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

If the triangle ABC is similar to the triangle PQR. Then find the value of PQ.

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