Triangles(10th Grade > Mathematics ) Questions and answers for exam Preparation

10th Grade > Mathematics

TRIANGLES MCQs

Total Questions : 58 | Page 1 of 6 pages

Question 1. In below shown figure,

\frac{P S}{S Q}

\frac{P T}{T R}

and

∠

PST=

∠

PRQ. Then

Δ

PQR is a/an __ triangle.

In Below Shown Figure, PSSQ= PTTR And∠PST= ∠PRQ. Then Δ...

Discuss Question

:
It is given that

\frac{P S}{S Q}

\frac{P T}{T R}

So, ST||QR [By converse of Basic Proportionality Theorem]

∴

∠

PST=

∠

PQR (Corresponding Angles)
Also, it is given that

∠

PST =

∠

PRQ
So,

∠

PRQ =

∠

PQR
Therefore, PQ = PR (Sides opposite the equal angles)
i.e.,

Δ

PQR is an isosceles triangle.

Question 2. In triangle ABC, D is a point on AB and E is a point on AC such that DE || BC. If

\frac{A D}{A B}

\frac{A E}{x}

, Then

x

is
___.

Discuss Question

:
In

△

ABC,
DE

∥

BC (Given)
Therefore,

\frac{A D}{A B}

\frac{A E}{A C}

[By Basic Proportionality Theorem]
Comparing the above with

\frac{A D}{A B}

\frac{A E}{x}

x

= AC

Question 3. In a right

△

ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does not give the ratio of the areas of

△

ABD and

△

ACB?

In A Right △ABC, A Perpendicular BD Is Drawn On to The L...

(ABAC)2
(ADAB)2
(BDCB)2
(ABAD)2

Discuss Question

Answer: Option D. -> (ABAD)2
:
D
Consider ΔABD andΔACB:

∠BAD = ∠BAC [common angle]
∠BDA = ∠ABC [

90^{\circ}

]
By AA similarity criterion,

△ A B D ~ △

ACB
Hence,

\frac{a r (Δ A B D)}{a r (Δ A C B)} = ({\frac{A B}{A C})}^{2} = ({\frac{A D}{A B})}^{2} = ({\frac{B D}{C B})}^{2}

Question 4. The ratio of the corresponding sides of two similar triangles is 1 : 3. The ratio of their corresponding heights is _________.

Discuss Question

Answer: Option A. -> 1:3
:
A
If two triangles are similar, then the ratio of the corresponding sides are equal.
Hence,
the ratio of heights = the ratio of sides = 1 : 3.

Question 5. In both the figures given below, all of the respective sides are equal and all interior angles are

90^{\circ}

. Are the figures shown below similar?

In Both The Figures Given Below, All Of The respective Side...

True
False
4.2 cm
0.525 cm

Discuss Question

Answer: Option A. -> True
:
A
Both the figures are similar as all the corresponding angles are equal and all the corresponding sides are in the same ratio as all the sides of both the figures are equal.
Ratio of corresponding sides =

\frac{4.2}{2.1} = 2

Question 6. A farmer had three land plots as shown. He has to divide the plots equally among 2 of his sons. He gives Area a and Area b to one of his son and third Area c to his second son. Did he give equal land plots to both of his son?
Enter True if he has given equal area else enter false.

True
False
81 : 16
16 : 81

Discuss Question

Answer: Option A. -> True
:
A
Pythagoras theorem states that

a^{2} + b^{2} = c^{2}

So he did correct i.e. he divided the land equally among his two sons.

Question 7. In

Δ A B C, A B = B C = 6 c m

. If a circle is drawn with center at B and radius 2 cm which intersects AB and BC at E and D, then

Δ A B C \sim Δ E B D

In ΔABC, AB=BC=6cm. If A Circle Is Drawn With Center At B ...

True
False
MB = 5 cm
AC = 5 cm

Discuss Question

Answer: Option A. -> True
:
A

Δ A B C a n d Δ E B D

\frac{B E}{B A} = \frac{B D}{B C} = \frac{2}{6} = \frac{1}{3} a n d ∠ D B E = ∠ A B C

.
By SAS similarity,

Δ A B C

and

Δ E B D

are similar.

Question 8. In

△

ABC,

∠ A a n d ∠ C

are given, the number of triangles that can be constructed with this data is -

One
Two
Three
Infinite

Discuss Question

Answer: Option D. -> Infinite
:
D

∠ S = 180^{o} - (∠ A + ∠ C)

The angles of the traingle are known. With the given measurement of the angles, we can draw infinite number of traingles (Similar triangles).

Question 9.

△ A B C

is such that

A B = 3 c m, B C = 2 c m

and

C A = 2.5 c m

△ D E F

is similar to

△ A B C

. If

E F = 4 c m

, then the perimeter of

△ D E F

is ____.

7.5 cm
15 cm
22.5 cm
30 cm

Discuss Question

Answer: Option B. -> 15 cm
:
B

\frac{A B}{D E}

\frac{A C}{D F}

\frac{B C}{E F}

\frac{2}{4}

\frac{1}{2}

D E = 2 \times A B = 6 c m, D F = 2 \times A C = 5 c m

∴

Perimeter of Δ D E F = (D E + E F + D F)

= 6 + 4 + 5 = 15 c m

Question 10. A ladder is resting on a wall of height 10

\sqrt{7}

m such that the foot of the ladder when placed 10

\sqrt{7}

m away from the wall, half of the ladder is extending above the wall. When the tip of the ladder is placed on the tip of the wall, how far is the foot of the ladder from the wall?