Basic proportionality theorem - class-X
| Description: basic proportionality theorem | |
| Number of Questions: 22 | |
| Created by: Avani Handa | |
| Tags: triangles similar triangles similarity similarity in geometrical shapes geometry maths |
Basic proportionality theorem is also known as
In $\triangle ABC,A-P-B, A-Q-C$ and $\overline {PQ} \parallel \overline {BC}$. If $PQ=5, AP=4$ and $PB=8$, then $BC=$.....
ABC is a triangle with AB = $13$ cm, BC =$14$ cm and CA=$15$ cm. AD and BE are the altitudes from A to B to BC and AC respectively. H is the point of intersection of the AD and BE. Then the ratio of $\frac { HD }{ HB } =$
In a triangle ABC, D and E are the point on the line segment BC and AC respectively, such that 2 BD = DC and 3 AE = 2 EC. The lines AD and BE meet at P,the line CP and AB F, then :
Let $ABC$ be a triangle and $D$ and $E$ be two points on side $AB$ such that $AD = BE$. If $D P | B C$ and $E Q | A C,$ then $P Q | A C.$
If the sides a, b, c, of a triangle are such that a: b: c: :1:$\sqrt{3}$: 2, then the A:B:C is -
In any $\Delta$ABC , $4\Delta(cotA+cotB+cotC)$ is equal to
$ABCD$ is a rectangl $P$ and $Q$ are poits on $AB$ and $BC$ respectively such that the area of triangle $APD=5$ area of triangle $PBQ=4$ and area of triangle $QCD=3$, all area in square units. THen the area of the triangle $DPQ$ in square units is
If G is the centroid of $\Delta ABC$ and if area of $\Delta AGB$ is 5 sq. nits then the area of $\Delta ABC$ is
The areas of two similar triangle are $18\ cm^{2}$ and $32\ cm^{2}$ respectively. What is the ratio of their corresponding sides?
In a triangle PQR, S and T are points on QR and PR respectively, such that QS = 3SR and PT = 4TR Let M be the point of intersection of PS and QT. FInd the ration QM : MT
In a triangle PQR, S and T are points on QR and PR respectively, such that QS = 3SR and PT = 4TR Let M be the point of intersection of PS and QT. FInd the ration QM : MT
If the areas of two similar triangles are equal, then they are congruent.
In a $\Delta ABC$, let $M$ be the mid-point of segment $AB$ and let $D$ be the foot of the bisector of $\angle C$. Then the ratio $\dfrac{Area\Delta CDM}{Area \Delta ABC}$ is $\left(A>B\right)$
If $\triangle ABC \cong \triangle QPR$ and $\dfrac {ar(\triangle ABC)}{ar(\triangle PQR)}=\dfrac {9}{4}$, $AB=18\ cm$ and $BC=15\ cm$, then $PR$ is equal to________ $cm$
The sides of a triangle are $3x+4y,\,4x+3y$ and $5x+5y$ units, where $x,y>0$.The triangle is ______________.
D and E are respectively the points on the sides AB and AC of a $\displaystyle \Delta ABC$ such that $AB = 12 cm$, $AD = 8 cm$, $AE = 12 cm$ and $AC = 18 cm$, then
Match the column.
| 1. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR},\angle A=\angle P$ | (a) AA similarity criterion |
|---|---|
| 2. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,$\displaystyle \angle A=\angle P,\angle B=\angle Q$ | (b) SAS similarity criterion |
| 3. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$$\angle A=\angle P$ | (c) SSS similarity criterion |
| 4. In $\displaystyle \Delta ACB,DE |
In an isosceles $\Delta A B C$ the base $A B$ is produced both the ways to $P$ and $Q$ such that $A P \times BO = A C ^ { 2 }$ then $\Delta A P C \sim \Delta B C Q$
In the sides $BC,CA,AB$ of a triangle $ABC$, three points $D,E,F$ are taken such that each of $BD,CE,AE$ is equal to one-third of the corresponding side, then
$\triangle DEF=\dfrac {1}{2}\triangle ABC$.
In any triangle, medians meet at a point and divide each other as the ratio of $2:3$
If $AD$ and $PM$ are medians of triangles $ABC$ and $PQR$, respectivetly where $\triangle ABC \sim \triangle PQR$, then $\dfrac {AB}{PR}=\dfrac {AC}{PM}$.