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Published on: 05/09/2019
The Triangle and Its Properties
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Questions + Answers key
Take MCQ Mathematics Test
1.
How many altitudes can a triangle have?
2.
Does a median lie wholly in the interior of the triangle? (If you think that this is not true, draw a figure to show such a case).
3.
Draw rought sketches of \(\triangle PQR\),where QE is a median.
4.
Classify the following triangles according to their angles.
5.
Find angle x in each figure.
6.
The two interior opposite angles of an exterior angle of a triangle are 60° and 80°. Find the measureof the exterior angle.
7.
An exterior angle of a triangle is of measure 70°and one of its interior opposite angles is of measure 25°. Find the measure of the other interior opposite angle.
8.
In the given \(\triangle MNP\), a line from vertex M is drawn passing through the side NP at O, such that the measure of angles are given. What would be the other name for OM?
9.
The exterior \(\angle ACD\ of \triangle ABC\) 1150.If \(\angle B=50^0\).then find \(\angle A.\ is\angle ACD>\angle A?\)
10.
Find the value of the unknown exterior angle x in the following diagrams.
11.
Which of the following cannot be the sides of a right triangle?
2 cm, 2 cm, 4 cm
5 cm, 12 cm, 13 cm
6 cm, 8 cm, 10 cm
3 cm, 4 cm, 5 cm
12.
In a \(\triangle ABC\) if \(\angle A=60^0\) and \(\angle B=30^0\) then the exterior angle formed by producing BC is equal to
180°
99°
90°
105°
13.
If the exterior angle of a triangle is 130° and its interior opposite angles are equal, then measure of each interior opposite angle is
55°
65°
50°
60°
14.
In the following figure, BC = CA and \(\angle A=20,\ then \angle ACD\) is equal to
30°
40°
60°
80°
15.
The perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm, is
42 cm
49 cm
89 cm
98 cm
16.
In an isosceles triangle, angles opposite to equal sides are______________.
17.
Median is also called___________in an equilateral triangle.
18.
The sum of an exterior angle of a triangle and its adjacent angle is always____________.
19.
In the following figure, value of x is___________.
20.
The line segment joining a vertex of a triangle to the mid-point of its opposite side is called its____________.
21.
In the following figure, the value of x is equal to 9cm.
22.
In the following figure, the value of y is equal to 90°.
23.
In the following figure, the value of x = 60°.
24.
Sum of the measures of three angles of a triangle is greater than 180°.
25.
Sum of any two angles of triangle is always greater than the third angle.
26.
In a \(\triangle ABC\), \(\angle A=120^0,\angle B=30^0\).The measure of \(\angle C\)is
27.
In a right angled triangle, atleast one angle should be equal to
28.
Equilateral triangle have each angle equals to
29.
Sum of interior opposite angles is.
30.
Sum of all three angles in a triangle is.
1.
Every triangle has three altitudes, one A from each vertex to the opposite side.
In the adjoining figure
\(AD\bot BC\),\(BE \bot AC\),and \(CF \bot AB\)
Therefore, line segments AD, BE and CF are three altitudes.
2.
Yes,a median lieswholly in the interior of the triangle.
3.
In the adjacent figure, we have \(\triangle PQR\) We know that, a median connects a vertex of a triangle to the mid-point of the opposite side. On joining Q and mid-point of PR, i.e. E.We get the required median QE.
4.
(i) \(\angle B=125^{0}\) which is greater than 90°, so it is an obtuse angled triangle.
(ii) All angles are smaller than 90°, so it is an acute angled triangle.
(iii) \(\angle B=90^{0}\), so it is a right angled rriangle.
5.
Let the given triangle be \(\triangle ABC\).Then, we have AB=AC
So, \(\triangle ABC\) is an isosceles triangle.
\(\therefore\angle B=\angle C\)
[since, the angle opposite to equal sides of an isosceles triangle are equal]
Also,\(\angle DAC\) is an exterior angle of \(\triangle ABC\).
Now, by exterior angle property of a triangle,
Sum of two interior opposite angles = Exterior angle
\(\Rightarrow\) x+x=110° \(\Rightarrow\) 2x=1100 = \(\frac{110^0}{2}=55^0\)
Hence, the value of x is 550.
6.
Given, two interior opposite angles are of measure 60° and 80°. By exterior angle property of a triangle,
Exterior angle = Sum of interior opposite angles
= 60° + 80° = 140°
Hence, the measure of the exterior angle is 140°.
7.
We know that, an exterior angle of a triangle is equal to the sum of its interior opposite angle.
Given, measure of an exterior angle = 70°
Measure of one interior opposite angle=25°
\(\angle ABC+\angle BAC=\angle ACD\)
\(\Rightarrow25^0+\angle BAC=70^0\)
\(\therefore\angle BAC=70^0-25^=45^0\)
Hence, the measure of the other interior opposite angle is 45°.
8.
In \(\triangle OMP\),
\(\angle OMP=\angle OPM\)
\(\therefore\) OM=OP.................1
[Since, sides opposite to equal angles are equal]
Also, in \(\triangle OMN\),
\(\angle OMN=\angle ONM\Rightarrow OM=ON\Rightarrow OP=ON\) [from Eq.1]
Hence, OM is the median of \(\triangle MPN\).
9.
\(\angle A=65^0,yes \angle ACD>\angle A\)
10.
(i)By exterior angle property of a triangle, Exterior angle = Sum of interior opposite angles
=> x = 50° + 70° = 120°
Hence, the exterior angle x is 120°.
(ii) By exterior angle property of a triangle,
Exterior angle = Sum of interior opposite angles
=> x=65°+45°=110°
Hence, the exterior angle x is 110°.
(iii) By exterior angle property of a triangle,
Exterior angle = Sum of interior opposite angles
=> x = 30° + 40° = 70°
Hence, the exterior angle x is 70°.
(iv) By exterior angle property of a triangle,
Exterior angle = Sum of interior opposite angles
=> x=60° +60° =120°
Hence, the exterior angle x is 120°.
(v) By exterior angle property of a triangle,
Exterior angle = Sum of interior opposite angles
\(\therefore\) x = 50° + 50° = 100°
Hence, the exterior angle x is 100°.
(vi) By exterior angle property of a triangle,
Exterior angle = Sum of interior opposite angles
=> x = 30° + 60° = 90°
Hence, the exterior angle x is 90°.
11.
22 + 22 = 8; 42 = 16 \(\therefore\) 22 + 22 \(\neq \) 42
12.
(c)
90°
13.
(b)
65°
14.
(b)
40°
15.
(d)
98 cm
16.
( )
equal
17.
( )
altitude
18.
( )
180°
19.
( )
90°
20.
( )
median
21.
(b)
22.
(a)
23.
(a)
24.
(b)
25.
(b)
26.
( )
30°
27.
( )
90°
28.
( )
60°
29.
( )
exterior angle
30.
( )
180°
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