Important Properties of Triangles

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. 1
2. 2
3. 3
4. 4

Q.

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

1. True
2. 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

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

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

3. $5$

4. $\sqrt{5}$

Q. Question 2
A triangle can be constructed by taking two of its angles as
a) ${110}^{\circ },{40}^{\circ }$
b) ${70}^{\circ },{115}^{\circ }$
c) ${135}^{\circ },{45}^{\circ }$
d) ${90}^{\circ },{90}^{\circ }$

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 triangle can be drawn if we know the length of one side of the triangle.

1. equilateral
2. isosceles
3. right

Q. In the given figure, find the measure of $\angle RQT$ if PQ = QR and $\angle QPR={60}^{\circ }$.

1. ${140}^{\circ }$
2. ${60}^{\circ }$
3. ${120}^{\circ }$
4. ${100}^{\circ }$

Q.

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

1. True

2. False

Q.

Which of the following angles can form a triangle ?

1. ${60}^{\circ },{105}^{\circ },{120}^{\circ }$

2. ${45}^{\circ },{85}^{\circ },{60}^{\circ }$

3. ${95}^{\circ },{15}^{\circ },{80}^{\circ }$

4. ${65}^{\circ },{105}^{\circ },{10}^{\circ }$

Q.

Why not aas and ssa used for cougruence rule.

Q. A triangle $\Delta$ PQR with $\angle Q={90}^{\circ }$, QR = 8 cm and PR = 10 cm is constructed. What would be the measure of PQ?

1. 4 cm
2. 10 cm
3. 6 cm
4. 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?

1. 5 cm

2. 6 cm

3. 2 cm

4. 1 cm​

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

1. Equilateral
2. Scalene
3. Right angled
4. Isosceles

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

1. h=a+b
2. $h^2=a^2+b^2$
3. h=a-b
4. $h^2=a^2-b^2$

Q. One angle of a right-angled triangle is 70${}^{\circ }$. Find the other acute angle.

1. ${20}^{\circ }$
2. ${40}^{\circ }$
3. ${30}^{\circ }$
4. ${60}^{\circ }$

Q.

Akash tried to make a $\Delta ABC$ 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 $\Delta$ABC, $\angle$A is 30${}^{\circ }$. The sides AB and AC are equal. Using constructions, find which side of $\Delta$ABC is the shortest.

1. AC

2. AB

3. Data Insufficient

4. BC

Q. A/An triangle can be drawn if we know the length of one side of the triangle.

1. equilateral
2. isosceles
3. right

Q.

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

1. equilateral

2. right-angled

3. obtuse-angled

4. acute-angled

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

1. A scalene triangle
2. An acute-angled triangle
3. A right-angled triangle
4. An obtuse-angled triangle

Q.

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

__

Q.

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

1. 20°, 40° and 60°

2. 40°, 60° and 80°

3. 60°, 80° and 100°

4. 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 _____.

1. Acute angled scalene triangle
2. Acute angled isosceles triangle
3. Right angled triangle
4. 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 $\angle$A = 50${}^{\circ }$

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 ?

1. Draw an arc of 7 cm with A as a Centre.
   
2. 
   Draw an arc of 7 cm with M as a Centre.
3. Draw a line segment of length of 7 cm from A
4. 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 $\Delta$ DEF?

1. $\Delta$ DEF has all its sides equal
2. $\Delta$ DEF is an isosceles triangle.
3. $\Delta$ DEF is a scalene triangle
4. $\Delta$ DEF is not an equilateral triangle

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