The Triangle And Its Properties(7th Grade > Mathematics ) Questions and answers for exam Preparation

7th Grade > Mathematics

THE TRIANGLE AND ITS PROPERTIES MCQs

Total Questions : 111 | Page 3 of 12 pages

Question 21. A triangle can have all the three angles greater than

60^{\circ}

True
False

Discuss Question

Answer: Option B. -> False
:
B
A triangle can't have all the three angles greater than

60^{\circ}

,because the sum of all the three angles of a triangle is

180^{\circ}

Question 22. If a

△

QPR is right angled at P, then which is the longest side of the triangle?

PQ
QR
PR
Can't be determined.

Discuss Question

Answer: Option B. -> QR
:
B
The side opposite to the greatest angle in a triangle is the longest.
Here the biggest angle is the right angle, hence QR is the longest side of the triangle.

If A △QPR Is Right Angled At P, Then Which is The Longest...

Question 23. Consider the figure:

Consider The Figure:If ∠A = 70∘, ∠ACD = 120∘, ...

∠

A =

70^{\circ}

∠

ACD =

120^{\circ}

, then the value of

∠

B (in degrees) is
___

Discuss Question

:
By Exterior Angle Property,

∠

ACD =

∠

A +

∠

∠

B =

∠

ACD -

∠

A
=

120^{\circ}

70^{\circ}

∠

B =

50^{\circ}

Question 24. 5cm, 12cm can be two sides of a right-angled triangle.

True
False
PR
Can't be determined.

Discuss Question

Answer: Option A. -> True
:
A
Sides of lengths 5cm, 12cm and 13cm form sides of aright angled triangle.

Question 25. If AM is a median of triangle ABC, then which of the following relation will always hold good?

AB + BC + CA = 2AM
AB + BC + CA > 2AM
AB + BC + CA
AB + BC + CA = AM

Discuss Question

Answer: Option B. -> AB + BC + CA > 2AM
:
B

If AM Is A Median Of Triangle ABC, Then Which Of The Followi...

Sum of lengths of any two sides of a triangle is always greater than the third side.
Hence,
AB + BM

>

AM
AC + CM

>

AM
Thus, AB + BC + CA

>

2AM

Question 26. Can we say that there exists only one triangle with a particular set of sides? What are such triangles known as? [2 MARKS]

Discuss Question

:
Nameand Explanation: 2 Marks
Yes, there exists a unique triangle for a particular set of sides. This is because 2 triangles having the same set of sides will be exactly identical. You can realize this by drawing 2 triangles with the same set of sides and then trying to superimpose one over the other. You will find that they are exactly identical.
If the two triangles have equal sides, then the two triangles are said to be congruent as equal sides are one of thecriteria for congruency of triangles.

Question 27. Can the following triangles exist? [3 MARKS]
(i) AB = 8 cm, BC = 6 cm, AC = 10cm
(ii) MN = 9 cm, NO = 5 cm, OM = 4 cm
(iii)

∠ A

175^{\circ}

∠ B

5^{\circ}

and

∠ C

0^{\circ}

Discuss Question

:
Each part: 1 Mark each
(i) Since AB + BC > AC, AB + AC > BC and BC + AC > AB, the following triangle can exist.
(ii) The following triangle cannot exist since OM + NO is not greater than MN.
(iii) The following triangle cannot exist since one of the angles of the triangles is 0

^{o}

. All angles of a triangle should be greater than 0

^{o}

Question 28. (a) If AB || DE, ∠AOD = 50° and ∠DPC = 160°, find the value of ∠DBE?

(b) A 15 m long ladder reached a window 12 m high from the ground when placed against a wall at a distance 'a'. Find the distance of the foot of the ladder from the wall.

[4 MARKS]

Discuss Question

:
(a)Steps: 1 Mark
Correct answer: 1 Mark
(b) Formula: 1 Mark
Result: 1 Mark
(a)

∠ O A D = 50 ° (g i v e n) ∠ D O C = 180 ° - 50 ° = 130 ° (l i n e a r p a i r) ∠ D P C = 160 ° (g i v e n) ∠ D P O = 180 ° - 160 ° (L i n e a r p a i r) ∠ D P O = 20 ° I n △ D O P ∠ O D P = 180 ° - (130 ° + 20 °) (b y a n g l e s u m p r o p e r t y) ∠ O D P = 30 ° I n △ D B E ∠ D B E = 180 ° - (90 ° + 30 °) (B y a n g l e s u m p r o p e r t y) ∠ D B E = 60 °

(b)

The wall and the ground are at right angle. Therefore the ladder,ground and the wall make the sides of a right-angled triangle.

∴ a^{2} + 12^{2} = 15^{2}

\Rightarrow a^{2} = 225 - 144 = 81

a = \sqrt{8} 1 = 9 m

Question 29. Answer the following: [2 MARKS]
(i) Angle opposite to CA in

Δ A B C

.
(ii) Side opposite to

∠ A

Δ A O D

Discuss Question

:
Each part: 1 Mark each
(i) In

Δ A B C

, opposite to side CA is the

∠ B

.
(ii) In

Δ A O D

∠ A

gets formed with AO and AD. Hence, the side opposite to

∠ A

will be OD.

Question 30. (a) Find x in the triangle given below if it is right-angled.

(b) Find x in the triangle given below if it is a right-angled triangle.

[3 MARKS]

Discuss Question

:
Formula: 1 Mark
Each part: 1 Mark
(a) Suppose, the above triangle is right-angled such that 10 is the longest side.
Then, according to Pythagoras Theorem,
Base