# Important Properties of Triangles

## Trending Questions

**Q.**If two angles of a triangle is 50 degree and 60 degree. Find the third angle.

**Q.**The diagonal of a rectangle produce by itself the same area as produced by its length and breadth - This is Baudhayan Theorem. Compare it with the Pythagoras property.

**Q.**How many triangles can be drawn if all the three sides are known?

- 1
- 2
- 3
- 4

**Q.**

It is possible to have a right-angled equilateral triangle. State whether the statement is True or False.

- True
- False

**Q.**

If the equation of base of an equilateral triangle is $2x-y=1$and the vertex $(-1,2)$, then the length of the side of the triangle is

$\sqrt{\frac{20}{3}}$

$\frac{2}{\sqrt{15}}$

$5$

$\sqrt{5}$

**Q.**Question 2

A triangle can be constructed by taking two of its angles as

a) 110∘, 40∘

b) 70∘, 115∘

c) 135∘, 45∘

d) 90∘, 90∘

**Q.**Question 1

A triangle can be constructed by taking its sides as

a) 1.8 cm, 2.6 cm, 4.4 cm

b) 2 cm, 3 cm, 4 cm

c) 2.4 cm, 2.4 cm, 6.4 cm

d) 3.2 cm, 2.3 cm, 5.5 cm

**Q.**A/An

- equilateral
- isosceles
- right

**Q.**In the given figure, find the measure of ∠RQT if PQ = QR and ∠QPR=60∘.

- 140∘
- 60∘
- 120∘
- 100∘

**Q.**

If you have three sides, you can always draw a triangle.

True

False

**Q.**

Which of the following angles can form a triangle ?

60∘, 105∘, 120∘

45∘, 85∘, 60∘

95∘, 15∘, 80∘

65∘, 105∘, 10∘

**Q.**

Why not aas and ssa used for cougruence rule.

**Q.**A triangle Δ PQR with ∠Q=90∘, QR = 8 cm and PR = 10 cm is constructed. What would be the measure of PQ?

- 4 cm
- 10 cm
- 6 cm
- 3 cm

**Q.**

Ram drew a line segment AB of length 3cm and another line segment CB of length 4cm which is perpendicular to line segment AB. What is the length of the third side of the triangle?

5 cm

6 cm

2 cm

1 cm

**Q.**If PQ = 5 cm, QR = 3.5 cm, and PR = 5 cm are joined. What type of triangle is this?

- Equilateral
- Scalene
- Right angled
- Isosceles

**Q.**If in a right-angled triangle 'h' is the hypotenuse, 'a' and 'b' are the perpendicular sides, then

- h=a+b
- h2=a2+b2
- h=a-b
- h2=a2−b2

**Q.**One angle of a right-angled triangle is 70∘. Find the other acute angle.

- 20∘
- 40∘
- 30∘
- 60∘

**Q.**

Akash tried to make a ΔABC whose rough figure is given below.

He first drew BC. Then taking B as a centre he drew 7cm arc and C as a centre he drew a 3cm arc.

Will he be able to get the point A? Yes or No.

**Q.**

In an isosceles ΔABC, ∠A is 30∘. The sides AB and AC are equal. Using constructions, find which side of ΔABC is the shortest.

AC

AB

Data Insufficient

BC

**Q.**A/An

- equilateral
- isosceles
- right

**Q.**

If the sides of a triangle are 3 cm, 4 cm, and 5 cm. Then, the triangle formed is a/an _____ triangle.

equilateral

right-angled

obtuse-angled

acute-angled

**Q.**To which of these triangles is the Pythagoras Theorem applicable?

- A scalene triangle
- An acute-angled triangle
- A right-angled triangle
- An obtuse-angled triangle

**Q.**

If line segment AB is perpendicular to CD then ∠DCA = ? (in degrees)

**Q.**

If the ratio of three angles of a triangle is 2: 3: 4, find the angles.

20°, 40° and 60°

40°, 60° and 80°

60°, 80° and 100°

100°, 120° and 140°

**Q.**A triangle XYZ is constructed such that XY = 2.5 cm, XZ = 5 cm and angle X = 65 degrees. Then triangle ABC is a/an _____.

- Acute angled scalene triangle
- Acute angled isosceles triangle
- Right angled triangle
- Equilateral triangle

**Q.**

Find the value of unknown exterior angle $x$ in the following diagram.

**Q.**Amit followed the following steps to construct a triangle △MAN such that MA = 4 cm, NA = 7 cm and ∠A = 50∘

Step 1:

Draw a line segment of MA of length 4 cm.

Step 2:

Measure the angle A with your protractor. Make a mark at 50 degrees and draw a line from A passing through the mark.

Step 3:

Mark the intersecting point as N.

Step 4:

Join MN to get the required △MAN.

Which of the step is missing for constructing this △MAN ?

- Draw an arc of 7 cm with A as a Centre.

Draw an arc of 7 cm with M as a Centre.- Draw a line segment of length of 7 cm from A
- Draw a line segment of length of 7 cm from M

**Q.**In a triangle two angles are equal. Prove that the triangles two sides are equal.

**Q.**A triangle is constructed as shown in the figure.

Which of the following is not correct about Δ DEF?

- Δ DEF has all its sides equal
- Δ DEF is an isosceles triangle.
- Δ DEF is a scalene triangle
- Δ DEF is not an equilateral triangle

**Q.**Find the length of diagonal of the rectangle whose sides are 16 cm and 12 cm.