Angles

Q.

In $\Delta ABC$, $\angle ACB={90}^{\circ }$, AB = C units, BC = a units, AC = b units, CD is perpendicular to AB and CD = p units. Then $\frac{1}{p^2}=$

1. Scalene

2. Isosceles but not right angled

3. Equilateral

4. Right Ðd & isosceles

Q.

A point O is taken inside an equilateral four sided figure ABCD such that its distances from the angular points D and B are equal. Show that AO and OC are in one and the same straight line. [3 MARKS]

Q.

Pedal triangle of an obtuse angled triangle lies

1. inside the triangle

2. outside the triangle

3. partially inside and partially outside the main triangle

4. Doesn't exist

Q. In the given figure, PQ>PR. QS and RS are the bisectors of $\angle Q$ and $\angle R$, respectively then which of the following is true?

1. $SQ>SR$
2. $\angle SRQ<\angle SQR$
3. $SQ=SR$
4. None of these

Q. Question 14
D and E are the mid-points of the sides AB and AC, respectively, of $\Delta ABC.DE$ is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is
(a) $\angle DAE=\angle EFC$
(b) $AE=EF$​​​​​​​
(c) $DE=EF$​​​​​​​
(d) $\angle ADE=\angle ECF$​​​​​​​

Q.

What is the angle formed between north and south direction?

1. Acute angle

2. Straight angle

3. Right angle

4. Obtuse angle

Q.

In $△ABC$, if AC $>$ AB, then which of the following options are correct?

1. C B

2. C B

3. C = B

4. None of these

Q. Question 5
In $\Delta PQR$, if $\angle R=\angle P$ and QR =4 cm and PR =5cm. Then, the length of PQ is
(A) 4 cm
(B) 5 cm
(C) 2 cm
(D) 2.5 cm

Q.

A _____________ is a mark of position. It has no size and shape.

Q.

In $△$ABC, AC $>$ AB and AD bisects $\angle$A. Which of the following option is correct?

1. ADC ADB

2. None of these

3. ADC = ADB

4. ADC ADB

Q. Question 3
In the given figure, if $AB||DE,\angle BAC={35}^{\circ }and\angle CDE={53}^{\circ },find\angle DCE.$

Q. What fraction does a clockwise revolution of the minute hand turn through, when it goes from 12 to 3?

1. 1/8
2. 1/3
3. 1/4
4. 1/6

Q. 39. Prove that the perpendicular lines drawn from two parallel lines are also parallel to each other?

Q.

If we have $\angle ABC$ as $\theta$, reflex $\angle ABC$ is equal to ________________.

1. 180º - θ

2. -180º + θ ​

3. 360º - θ

4. 360º + θ

Q. In a five sided star formed by line segments prove that the sum of all angles is equal to 180.

Q. In right angled Triangle ABC if $D$ and $E$ trisect $BC$ then prove that $8A{E}^2=3A{C}^2+5A{D}^2$

Q. For making an angle of 105${}^{\circ }$, it is mandatory to construct 60${}^{\circ }$.

1. True
2. False

Q.

Consider the figure:

If $\angle A={50}^{\circ }$​, $\angle B={70}^{\circ }$​, and $x=2y,$ then find the value of $x+2y.$

1. ${160}^{\circ }$

2. ${170}^{\circ }$

3. ${80}^{\circ }$

4. ${90}^{\circ }$

Q.

Consider the figure:
If $\angle A={50}^{\circ }$​, $\angle B={70}^{\circ }$​, and $x=2y,$ then find the value of $x+2y.$ [2 Marks]

Q.

In Fig. PQ > PR. QS and RS are the bisectors of $\angle$Q and $\angle$R respectively

Prove that SQ>SR

Q.

The value of the exterior angle of a triangle is equal to the sum of __?

1. the other two exterior angles of a triangle

2. all the interior angles of a triangle

3. the value of external angles of a triangles cannot be found

4. the two opposite interior angles

Q.

In $△$ABC, if $\angle$A = ${45}^{\circ }$ and $\angle$B = ${70}^{\circ }$, then the shortest and the longest sides of the triangle, respectively, are:

1. AB, BC

2. BC, AC

3. None of these

4. AB, AC

Q. In the given fig $AD$ divides $\angle BAC$ in the ratio $1:3$ and $AD=DB$. Determine the value of $x.$

Q. Where will the hand of a clock stop if it:
Start at $3$ and makes $\frac{1}{2}$ of a revolution, clockwise?

Q.

In the given figure, PQ>PR. QS and RS are the bisectors of $\angle Q$ and $\angle R$, respectively then which of the following is true?

1. None of these

2. $SQ>SR$

3. $\angle SRQ<\angle SQR$

4. $SQ=SR$

Q. Where will the hand of a clock stop if it:
Start at $4$ and makes $\frac{3}{4}$ of a revolution, clockwise?

Q.

In Fig. AC = AE, AB = AD and $\angle$ BAD = $\angle$ EAC. Prove that BC = DE.
[2 MARKS]

Q. If lines PQ and RS intersect at point T, such that $\angle PRT={40}^{\circ }$, $\angle RPT={95}^{\circ }$ and $\angle TSO={75}^{\circ }$ , find $\angle SQT$.

Q.

In the following figure, AD=??

1. BD

2. CE

3. AE

4. None of these

Q.

In the given figure, AM $\perp$ BC and AN is the median from $\angle$A. Then,

1. 

2. 

3. 

4.