Similar Triangles and Their Properties - Class X
Properties of similar triangles including Basic Proportionality Theorem, area ratios, side ratios, similarity criteria, and triangle geometry
Questions
Basic proportionality theorem is also known as
- Basic theorem
- Thales Theorem
- Potential theorem
- Unknown
In $\triangle ABC,A-P-B, A-Q-C$ and $\overline {PQ} \parallel \overline {BC}$. If $PQ=5, AP=4$ and $PB=8$, then $BC=$.....
- $6$
- $10$
- $12.5$
- $15$
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 $\frac { HD }{ HB } =$
- $\dfrac { 3 }{ 5 } $
- $\dfrac { 12 }{ 13 } $
- $\dfrac { 4 }{ 5 } $
- $\dfrac { 5 }{ 9 } $
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 :
- AP:PD = 2:1
- BP : PE =4:
- BP:PE =5:4
- CP:PF = 7:2
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 $P Q | A C.$
- True
- False
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 -
- 3 : 2 : 1
- 3 : 1 : 2
- 1 : 3 : 2
- 1 : 2 : 3
In any $\Delta$ABC , $4\Delta(cotA+cotB+cotC)$ is equal to
- $3(a^2+b^2+c^2)$
- $2(a^2+b^2+c^2)$
- $(a^2+b^2+c^2)$
- none of these
$ABCD$ 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
- $12$
- $\dfrac {20}{3}$
- $2\sqrt {21}$
- $\sqrt {21}$
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
- 20 sq. unit
- 10 sq.unit
- 15 sq. unit
- 25 sq. unit
The areas of two similar triangle are $18\ cm^{2}$ and $32\ cm^{2}$ respectively. What is the ratio of their corresponding sides?
- $3:4$
- $4:3$
- $9:16$
- $16:9$
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
- 15: 8
- 16 : 5
- 15 : 4
- 5 : n2
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
- 15 : 8
- 16 : 5
- 15 : 4
- 5 :2
If the areas of two similar triangles are equal, then they are congruent.
- True
- False
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________ $cm$
- $10$
- $12$
- $20/3$
- $8$
The sides of a triangle are $3x+4y,,4x+3y$ and $5x+5y$ units, where $x,y>0$.The triangle is ______________.
- right angled
- equilateral
- obtuse angled
- none of these
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
- DE $\parallel$ BD is true
- DE $\parallel$ BC is true
- AD $\parallel$ BD is true
- AD $\parallel$ CD is true
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 |
- $\displaystyle 1\rightarrow a,2\rightarrow b,3\rightarrow c,4\rightarrow d$
- $\displaystyle a\rightarrow d,2\rightarrow a,3\rightarrow c,4\rightarrow b$
- $\displaystyle 1\rightarrow b,2\rightarrow a,3\rightarrow c,4\rightarrow d$
- $\displaystyle 1\rightarrow c,2\rightarrow b,3\rightarrow d,4\rightarrow a$