Congruent Triangles

Q. In the given figure, $\angle ABC={69}^{\circ },\angle ACB={31}^{\circ }.Find\angle BDC$

Q. Question 7
In $\Delta ABCand\Delta DEF,\angle B=\angle E,\angle F=\angle C$ and AB = 3DE. Then the two triangles are

(A) Congruent but not similar
(B) Similar but not congruent
(C) Neither congruent not similar
(D) Congruent as well as similar

Q.

$△RST\sim △XYZ.$ In $△RST$, $RS=4.5$ cm, $\angle RST={40}^{\circ }$, $ST=5.7$ cm Construct $△RST$ and $△XYZ$, such that $\frac{RS}{XY}=\frac{3}{5}$.

Q. $\text{If}\Delta ABC\sim \Delta PQR\text{and}$ $\Delta PQR\sim \Delta XYZ,\text{then}$ $\Delta ABC\sim \Delta XYZ$

1. True
2. False

Q. Figures are congruent when they have the same size and same .

Q. In Fig. 7.136, $\Delta ACB\sim \Delta APQ$. If BC = 8 ~cm, [Q = 4 ~cm, BA = 6.5 cm and P= 2.8 cm, find CA and AQ.

Q. If $\Delta PQR$ is a obtuse triangle with $\angle Q$ as the obtuse angle, then the measure of $\angle Q>{90}^o$ and measure of $\angle P$ and measure of $\angle R$ is:

1. $>{90}^o$
2. $>{180}^o$
3. $<{90}^o$
4. $<{180}^o$

Q. $\text{If}\Delta ABC\sim \Delta PQR\text{and}$ $\Delta PQR\sim \Delta XYZ,\text{then}$ $\Delta ABC\sim \Delta XYZ$

1. True
2. False

Q. $△ABC\sim △DEF$ and their perimeters are 32 cm and 24 cm respectively. If AB = 10 cm, find $10DE$(in cm).

Q. $\text{If}\Delta ABC\sim \Delta PQR\text{and}$ $\Delta PQR\sim \Delta XYZ,\text{then}$ $\Delta ABC\sim \Delta XYZ$

1. True
2. False

Q.

In the $∆\mathrm{ABC},\mathrm{AB}\cong \mathrm{BC}\cong \mathrm{AC}$.

What kind of triangle is this?

Q. There exist two triangles such that there five parts ( i.e. three angles and two sides) are congruent to each other but yet the triangles are not congruent ?

1. True
2. False

Q. $\Delta ABC\sim \Delta PQR$. If $\angle B$ of $\Delta ABC$ and $\angle R$ of $\Delta PQR$ are ${60}^{\circ }$, then $\angle$ RPQ =

1. ${120}^{\circ }$
2. ${60}^{\circ }$
3. ${30}^{\circ }$

Q. $\Delta ABC\sim \Delta PQR$. If $\angle B$ of $\Delta ABC$ and $\angle R$ of $\Delta PQR$ are ${60}^{\circ }$, then $\angle$ RPQ =

1. ${120}^{\circ }$
2. ${60}^{\circ }$
3. ${30}^{\circ }$

Q. Find the measure of ∠R from the given figure.

Q. A circle is inscribed in a quadrilateral ABCD in which $\angle B={90}^o$. If $AD=23cm$, $AB=29cm$ and $DS=5cm$. Find the radius of the circle.

1. $13$ cm
2. $11$ cm
3. $9$ cm
4. None of these

Q. In $\Delta ABC$ and $\Delta DEF,AB=DF$ and $\angle A=\angle D$. The two triangles will be congruent by SAS
axiom if :

1. BC $=$ EF
2. AC $=$ DE
3. BC $=$ DE
4. AC $=$ EF

Q. $S$ and $T$ are points on sides $PR$ and $QR$ of $\Delta PQR$ such that $\angle P=\angle RTS$. Show that $\Delta PRQ\sim \Delta RTS$.

Q. In the given figure, PQ = PS. The value of x is

Q. In any right angled triangle $ABC$, right angle at $\angle A$. If $AB=100\sqrt{3},AC=100$. Find angle $C$.

1. ${30}^{\circ }$
2. ${60}^{\circ }$
3. ${45}^{\circ }$
4. ${120}^{\circ }$

Q. How many triangles are there in the given figure?

1. 13
2. 11
3. 10
4. 15

Q.

If $AB\mathit{=}DE\mathit{,}\mathit{}BC\mathit{=}EF$ and $AC\mathit{=}DF$ then $∆ABC\cong$ ______________.

Q. In the figure which of the following given correspondence between the vertices of two triangles are similarity.
(P) correspondence ABC $\leftrightarrow$ DEF
(Q) correspondence ABC $\leftrightarrow$ FDE
(R) correspondence ABC $\leftrightarrow$ EFD

1. P and R are correct
2. Only P is correct
3. Q and R are correct
4. P, Q and R are correct

Q. $\Delta ABC\sim \Delta PQR$. If $\angle B$ of $\Delta ABC$ and $\angle R$ of $\Delta PQR$ are ${60}^{\circ }$, then $\angle$ RPQ =

1. ${120}^{\circ }$
2. ${60}^{\circ }$
3. ${30}^{\circ }$

Q. In Fig. 7.136, $\Delta ACB\sim \Delta APQ$. If BC = 8 ~cm, [Q = 4 ~cm, BA = 6.5 cm and P= 2.8 cm, find CA and AQ.

Q. $\Delta ABC\sim \Delta PQR$. If $\angle B$ of $\Delta ABC$ and $\angle R$ of $\Delta PQR$ are ${60}^{\circ }$, then $\angle$ RPQ =

1. ${120}^{\circ }$
2. ${60}^{\circ }$
3. ${30}^{\circ }$