Triangles

Q.

The interior angles of a polygon are in arithmetic progression.

The smallest angle is 120^•and the common difference is 5.

Find ND the number of sides of polygon.

Q. 18 )The area of the triangle formed by the line x/2+ y/5= 1 with both the axes is (1) 10 sq. units (2) 5 sq. units (3) 18 sq. units (4) 7 sq.units

Q.

Find the sum of all the exterior angles of a triangle.

1. 60°

2. 90°

3. 360°

4. 180°

Q.

A polygon with minimum number of sides is :

1. Triangle

2. Angle

3. Pentagon

4. Square

Q.

Prove that each angle of an equilateral triangle is ${60}^{\circ }$

Q.

The sides BC, CA and AB of $\Delta ABC$ are produced in order to form exterior angles $\angle ACD$ , $\angle EAB$, and $\angle CBF$. If $x+y+z={180}^{\circ }$ then $\angle ACD+\angle CBF+\angle EAB$ is

1. ${180}^{\circ }$

2. ${270}^{\circ }$

3. ${360}^{\circ }$

4. ${540}^{\circ }$

Q. How a median is different from a perpendicular bisector of a triangle.

Q.

In $\Delta ABC,$ AD is the median, find the length of AD if AC =7 cm, BC =8 cm and AB =9 cm.

​​

1. 8 cm

2. 7 cm

3. $7\sqrt{5}cm$

4. $8\sqrt{5}cm$

Q. In $∆$PQR, $\angle$Q = 90^° , PQ = 12, QR = 5 and QS is a median. Find l(QS).

Q. 8. The radii of two concentric circles are 13 cm and 8 cm. AB is the diameter of a bigger circle and BD is tangent to the smaller circle touching it at D and intersecting the larger circle at P , on producing find the length of AP

Q.

In $\Delta ABC$; $BM\perp AC$ and $CN\perp AB$;

Then, $\frac{AB}{AC}=\frac{BM}{CN}=\frac{AM}{AN}$

1. True

2. False

Q. Which of the following statements are true (T) and which are false (F):

(i) Sum of the three angles of a triangle is 180°.

(ii) A triangle can have two right angles.

(iii) All the angles of a triangle can be less than 60°

(iv) All the angles of a triangle can be greater than 60°.

(v) All the angles of a triangle can be equal to 60°.

(vi) A triangle can have two obtuse angles.

(vii) A triangle can have at most one obtuse angles.

(viii) If one angle of a triangle is obtuse, then it cannot be a right angled triangle.

(ix) If one angle of a triangle is obtuse, then it cannot be a right angled triangle.

(x) An exterior angle of a triangle is less than either of its interior opposite angles.

(xi) An exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Q.

One of the angles of a triangle is 75^o. If the difference of the other two angles is 35^o, then the larger angle of the other two angles of the triangle has a measure of:

1. 80^o

2. 100^o

3. 135^o

4. 70^o

Q. Side BC of a triangle ABC has been produced to a point D such that ∠ACD = 120°. If ∠B = $\frac{1}{2}$ ∠A is equal to

(a) 80°

(b) 75°

(c) 60°

(d) 90°

Q.

In the given figure, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar (ACE) [2 MARKS]

Q. AB is the diameter of a semicircle.Through A draw any straight line lines AP, AQ to meet the circumference again at P and Q. Draw PM, QN perpendicular to AB.Then the ratio AM:AN is equal to A) BP^2: BQ^2 B) AP^2 : AQ^2 C) AP^2 : BQ^2 D) none of these

Q.

An exterior angle of a triangle is 110^o; and one of the interior opposite angles is 30^o, then the other two angles of the triangle are

1. 60^o, 70^o

2. 50^o, 60^o

3. 120^o, 80^o

4. 70^o, 80^o

Q.

In the given figure, AM $\perp$ BC and AN is the bisector of $\angle$A. Then $\angle$MAN is

1. $16{\frac{1}{2}}^{\circ }$

2. $32{\frac{1}{2}}^{\circ }$

3. ${16}^{\circ }$

4. ${32}^{\circ }$

Q.

$△\mathrm{ABC}$ is a right-angled triangle in which $\angle A=90°$ and $AB=AC$. Find $\angle B$ and $\angle C$.

Q. The difference between the largest and the smallest angle of the given triangle is:

1. $\angle B-\angle C$
2. $\angle C-\angle B$
3. $\angle B-\angle A$
4. $\angle A-\angle B$

Q. In a triangle ABC a circle is inscribed sides of ABC are touching thecircle externallyatP Q R .IF AP=4cm BP=6cm AC=12cm then find radius of circl

Q. 40. Mid Points of the sides AB and AC of a Triangle ABC are (3, 5) (-3, -3) respectively then the length of the side BC is

Q. 3. The midpoints of sides of triangles are (3, 2), (-1, -2) and (5, -4). Find the coordinates of the vertices of a triangle and then fond its area.

Q. a circle is inscribed within a quadrilateral ABCD touching sides AD, AB, BC, and CD at points P, Q, R and S respectively. if BC =14cm , BQ=8cm and DC=18cm and AD\perp DC, then find the radius of thr circle

Q.

The measures of three angles of a triangle are in the ratio 1: 2: 3. Then the triangle is

1. Equilateral

2. Obtuse angled

3. Isosceles

4. Right angled

Q.

Write the converse theorem of angles opposite to equal sides of an equilateral triangle are equal.

Q. Question 4
In the given figure, ABC and ABD are two triangles on the same base AB. If line-segment CD is bisected by AB at O, show that ar(ABC) = ar(ABD).

Q.

A triangle cannot have more than______right angle(s).

Q. Atmost how many obtuse angle(s) can we have in a triangle?

1. 2
2. 1
3. 0
4. 3

Q. { If }C_1:x^2+y^2=(3+2\sqrt2)^2 be a circle. }PA and }PB}{ are pair of tangents on }C_1 where }P is any point on the }}{ director circle of }C_1, then the radius of the smallest }}{ circle which touches }C_1 externally and also the two }}{ tangents }PA and }PB is