1 → B, 2 → A, 3 → C, 4 → D

1 → A, 2 → B, 3 → C, 4 → D

1 → D, 2 → A, 3 → C, 4 → B

1 → B, 2 → A, 3 → C, 4 → D

1 → C, 2 → B, 3 → D, 4 → A.

Important Questions: Triangles for Class 10 Maths

Important Questions: Triangles - Question 1

In the given figure, △ABC is a right-angled triangle with ∠BAC=90^∘. The perpendicular from A to BC meets BC at D. Which of the following relations is true?

A.
BD . CD = BC²
B.
AB . AC = BC²
C.
BD . CD = AD²
D.
AB . AC = AD²

Detailed Solution: Question 1

Important Questions: Triangles - Question 2

In the given figure, AD/BD = AE/EC and ∠ADE = 70°, ∠BAC = 50°, then angle ∠BCA =

A.
70°
B.
50°
C.
80°
D.
60°

Detailed Solution: Question 2

The correct option is Option D.

By using angle sum property, we find third angle

AED = 180° - (70°+50°) = 60°

and DE ll BC

So, by corresponding angle, we get the value of BCA = 60°.

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Important Questions: Triangles - Question 3

If ΔABC ~ ΔEDF then which of the following is not true?

A.
BC . EF = AC . FD
B.
AB . EF = AC . DE
C.
BC . DE = AB . EF
D.
BC . DE = AB . FD

Detailed Solution: Question 3

Since △ABC~△EDF

Then, AB/ED = BC/DF = AC/EF

A) BC/DF = AC/EF

⇒BC.EF=AC.FD

So, A) is true

B) AB/ED = AC/EF

⇒AB.EF=AC.DE

So,B) is true

D) AB/ED = BC/DF

BC.DE=AB.EF

So, D) is not true

Therefore, Option C is not true

Important Questions: Triangles - Question 4

Which pair of the given quadrilaterals is similar?

A.
I only
B.
III only
C.
I and III
D.
IV

Detailed Solution: Question 4

Quadrilaterals are similar if their angles are equal and corresponding sides are proportional, which is only in figures I and III. Thus, option c is correct

Important Questions: Triangles - Question 5

D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then length of DE (in cm) is

A.
3 cm
B.
7cm
C.
1 cm
D.
2 cm

Detailed Solution: Question 5

Since, DE is parallel to BC

→ angle ADE = angle ABC (corresponding angles)

→ angle AED = angle ACB (corresponding angles)

Hence, by AA criterion of similarity,

∆ADE ~ ∆ABC

ratio of corresponding sides of similar triangles are equal.

AD/AB = DE/BC

AB = AD + DB

AB = 2 + 3 = 5 cm

So,

2/5 = DE/7.5

DE = 2/5 × 7.5

DE = 2 × 1.5

DE = 3 cm.

Important Questions: Triangles - Question 6

If in two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ , then

A.
ΔPQR ~ ΔCAB
B.
ΔPQR ~ ΔABC
C.
ΔCBA ~ ΔPQR
D.
ΔBCA ~ ΔPQR

Detailed Solution: Question 6

Then, ΔCAB ~ ΔPQR

Important Questions: Triangles - Question 7

If ΔPRQ ~ ΔXYZ, then which of the following correctly represents the relationship between their corresponding sides?

Detailed Solution: Question 7

Since ΔPRQ ~ ΔXYZ, the vertices correspond in order: P → X, R → Y, and Q → Z. This means the corresponding sides are:
- PR corresponds to XY,
- RQ corresponds to YZ,
- PQ corresponds to XZ.
In similar triangles, corresponding sides are proportional. Therefore, the ratios of the lengths of corresponding sides are equal, such as:
PQ / XZ = QR / YZ.
Option (c) correctly reflects this proportionality. Note that side names are written in order of their endpoints, so QR is the same side as RQ but written reversed; however, the correspondence is between RQ and YZ, so using QR or RQ must be consistent with the order of vertices.

Important Questions: Triangles - Question 8

Match the column:

A.
1 → A, 2 → B, 3 → C, 4 → D
B.
1 → D, 2 → A, 3 → C, 4 → B
C.
1 → B, 2 → A, 3 → C, 4 → D
D.
1 → C, 2 → B, 3 → D, 4 → A.

Detailed Solution: Question 8

1. In ΔABC and ΔPQR, given AB/PQ = AC/PR and ∠A = ∠P, by SAS similarity criterion, ΔABC ~ ΔPQR. 2. In ΔABC and ΔPQR, given ∠A = ∠P, ∠B = ∠Q, by AA similarity criterion, ΔABC ~ ΔPQR. 3. In ΔABC and ΔPQR, given AB/PQ = AC/PR = BC/QR, by SSS similarity criterion, ΔABC ~ ΔPQR. 4. In ΔABC, DE || BC implies by Basic Proportionality Theorem (BPT) that AD/BD = AE/CE.Therefore, the correct matching is: 1 → B (SAS similarity criterion), 2 → A (AA similarity criterion), 3 → C (SSS similarity criterion), 4 → D (BPT).

Important Questions: Triangles - Question 9

In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are

A.
Congruent but not similar
B.
Similar but not congruent
C.
Neither congruent nor similar
D.
Congruent as well as similar

Detailed Solution: Question 9

to be congruent, the conditions are
S S S - three sides
S A S - two sides and the included angle
A S A - two angles and one side
R H S - R H S - Right angle, Hypotenuse and one side
But to be similar,
A A A means 3 angles
A A means only two angles ....
in both triangles should be equal.
In the problem, equality of two angles is given, but equality of sides is not given.
So, given triangles are not congruent.
But they are similar.

Important Questions: Triangles - Question 10

ABC and BDE are two equilateral triangles such that D is mid-point of BC. Ratio of the areas of triangles ABC and BDE is

A.
2 : 1
B.
1 : 4
C.
1 : 2
D.
4 : 1

Detailed Solution: Question 10

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Important Questions: Triangles - Free MCQ Test with solutions for

MCQ Practice Test & Solutions: Important Questions: Triangles (10 Questions)

In the given figure, △ABC is a right-angled triangle with ∠BAC=90^∘. The perpendicular from A to BC meets BC at D. Which of the following relations is true?

In the given figure, AD/BD = AE/EC and ∠ADE = 70°, ∠BAC = 50°, then angle ∠BCA =

If ΔABC ~ ΔEDF then which of the following is not true?

Which pair of the given quadrilaterals is similar?

D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then length of DE (in cm) is

If in two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ , then

If ΔPRQ ~ ΔXYZ, then which of the following correctly represents the relationship between their corresponding sides?

Match the column:

In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are

ABC and BDE are two equilateral triangles such that D is mid-point of BC. Ratio of the areas of triangles ABC and BDE is

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Important Questions: Triangles - Free MCQ Test with solutions for

MCQ Practice Test & Solutions: Important Questions: Triangles (10 Questions)

In the given figure, △ABC is a right-angled triangle with ∠BAC=90∘. The perpendicular from A to BC meets BC at D. Which of the following relations is true? ​

In the given figure, AD/BD = AE/EC and ∠ADE = 70°, ∠BAC = 50°, then angle ∠BCA =

If ΔABC ~ ΔEDF then which of the following is not true?

Which pair of the given quadrilaterals is similar?

D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then length of DE (in cm) is

If in two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ , then

If ΔPRQ ~ ΔXYZ, then which of the following correctly represents the relationship between their corresponding sides?

Match the column:

In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are

ABC and BDE are two equilateral triangles such that D is mid-point of BC. Ratio of the areas of triangles ABC and BDE is

Mathematics (Maths) Class 10

Mathematics (Maths) Class 10

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About this Class 10 Practice Test

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In the given figure, △ABC is a right-angled triangle with ∠BAC=90^∘. The perpendicular from A to BC meets BC at D. Which of the following relations is true?