# Triangles

## Trending Questions

**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.

60°

90°

360°

180°

**Q.**

A polygon with minimum number of sides is :

Triangle

Angle

Pentagon

Square

**Q.**

Prove that each angle of an equilateral triangle is 60∘

**Q.**

The sides BC, CA and AB of ΔABC are produced in order to form exterior angles ∠ACD , ∠EAB, and ∠CBF. If x+y+z=180∘ then ∠ACD+∠CBF+∠EAB is

180∘

270∘

360∘

540∘

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

**Q.**

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

8 cm

7 cm

7√5cm

8√5cm

**Q.**In $\u2206$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 ΔABC; BM⊥AC and CN⊥AB;

Then, ABAC=BMCN=AMAN

True

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:

80

^{o}100

^{o}135

^{o}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

60

^{o}, 70^{o}50

^{o}, 60^{o}120

^{o}, 80^{o}70

^{o}, 80^{o}

**Q.**

In the given figure, AM ⊥ BC and AN is the bisector of ∠A. Then ∠MAN is

1612∘

3212∘

16∘

32∘

**Q.**

$\u25b3\mathrm{ABC}$ is a right-angled triangle in which $\angle A=90\xb0$ and $AB=AC$. Find $\angle B$ and $\angle C$.

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

- ∠B−∠C
- ∠C−∠B
- ∠B−∠A
- ∠A−∠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

Equilateral

Obtuse angled

Isosceles

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?

- 2
- 1
- 0
- 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