SAS Similarity

Q.

If two sides of a triangle are proportional to two sides of another triangle then the triangles are similar.

1. True

2. False

Q.

In the given figure, $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and$\angle$PST= $\angle$PRQ, then $\Delta$PQR is _______triangle.

1. an Isosceles

2. a Right angled

3. a Scalene

4. an Equilateral

Q. In the given figure, $\frac{QR}{QS}=\frac{QT}{PR}and$ $\angle 1=\angle 2$. Which of the following is true?

1. $\Delta PSQ\sim \Delta TQR$
2. $\Delta QPS\sim \Delta TQR$
3. $QSP\sim \Delta TQR$
4. $\Delta PQS\sim \Delta TQR$

Q.

In the adjoining figure, two triangles FGH and QPR are:

1. Similar using AA criteria

2. Similar using SAS criteria

3. Not similar

4. None of these

Q. Question 6
It is given that $\Delta ABC\cong \Delta RPQ$. It is true to say that BC = QR ? why?

Q.

$\text{In the figure, PQ || AB, CQ = 6 cm,}\text{CB = 8 cm. If CP = 7 cm,}\text{then what is the length of AC?}$

1. $8cm$
2. $9cm$
3. $\frac{25}{4}cm$
4. $\frac{28}{3}cm$

Q. In $\Delta ABC,AB=BC=6cm$. If a circle is drawn with centre at B and radius 2 cm which intersects AB and BC at E and D respectively, then:

1. $\frac{AB}{EB}=\frac{BC}{ED}$
2. $\frac{AB}{EB}=\frac{AC}{ED}$
3. $\Delta ABC\sim \Delta EBD$
4. $\Delta BAC\sim \Delta EBD$

Q. What will be the measure of $\angle$PQR,
if $\angle$ZXY = 25° ?

1. 10°
2. 25°
3. 15°
4. 35°

Q. Question 7 (ii)
P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP. show that:
$\left(ii\right)ar\left(RQC\right)=\frac{3}{8}ar\left(ABC\right)$

Q. In adjoining figure, $AP\perp BC,AD\parallel BC$, then find
$A\left(△ABC\right):A\left(△BCD\right)$

Q.

In the adjoining figure, the lines l, m and n are parallel to each other, and G is mid-point of CD. Calculate:

(i) BG if AD = 6 cm

(ii) CF if GE = 2.3 cm

(iii) AB if BC = 2.4 cm

(iv) ED if FD = 4.4 cm

Q.

In an isosceles $\Delta ABC$, the base AB has produced both ways in P and Q such that $AP\times BQ=A{C}^2$.

Prove that $\Delta ACP\sim \Delta BCQ$.

(3 Marks)

Q.

In the figure, if $\angle B=\angle Q$, then:

1. $△ABC\sim △PQR$

2. $△ABC\sim △RQP$

3. $△CBA\sim △QPR$

4. $△CBA\sim △QPR$

Q.

In the figure below, if the line segment ST is parallel to line segment QR such that $\frac{PS}{SQ}=\frac{PT}{TR}$. This provided data is not sufficient to prove that
$\frac{ST}{QR}=\frac{PT}{TR}$

1. False

2. True

Q.

In the figure, AC = 10cm, PC = 15cm, PQ = 12cm, find PB.

1. 6cm

2. 7cm

3. 8cm

4. 9cm

Q. In the figure, diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O.
$\text{Prove that}ar\left(△AOD\right)=ar\left(△BOC\right).$

Q. In a $△ABC$, if $3\angle A=4\angle B=6\angle C$, calculate the angles.

Q. In given Figure, If $△ABE\cong △ACD$, then prove that $△ADE\sim △ABC$

Q.

In the following figure, AB = AC = AD, $△$ABC $\cong$ $△$ACD if ___.

1. BC = CD

2. BC = AD

3. BC = AC

4. CD = AC

Q.

In $\Delta ABC,AB=BC=6cm$. If a circle is drawn with center at B and radius 2 cm which intersects AB and BC at E and D, then $\Delta ABC\sim \Delta EBD$.

1. True

2. False

Q. State true or false:

1. True
2. False

Q. In $\Delta ABC$ $DE\parallel BC$ Find $AD$ if $DB=$$7.2$ cm, $AE=1.8$ cm, and $EC=5.4$ cm.

Q. In $\Delta ABC$, AB = BC = 6 cm. If a circle is drawn with center at B and radius 2 cm which intersects AB and BC at E and D, then show that $\Delta ABC\sim \Delta EBD$.

Q. Three girls Reshma, salma and Mandip are playing a game by standing on a circle of radius $5m$ drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and berween Salma and Mandip is $6m$ each, what is the distance between Reshma and Mandip?

Q. State which pair of triangles in figure are similar. Write the similarity criterion used by you for answering the question.

1. $SSS$
2. $SAS$
3. $AAA$
4. None of these

Q.

$\text{In the figure, PQ || AB, CQ = 6 cm,}\text{CB = 8 cm. If CP = 7 cm,}\text{then what is the length of AC?}$

1. $8cm$
2. $9cm$
3. $\frac{25}{4}cm$
4. $\frac{28}{3}cm$

Q. Question 5 (v)
In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that:

(v) ar(BFE) = 2ar(FED)

Q. $AO:OB$

1. $1:2$
2. $3:5$
3. $3:2$
4. $3:8$

Q. In the figure, diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O.
$\text{Prove that}ar\left(△AOD\right)=ar\left(△BOC\right).$

Q. In the figure, $\angle$ACB $={42}^o$, find $\hat{x}$.