Congruence and Similarity MCQ Quiz in मल्याळम - Objective Question with Answer for Congruence and Similarity - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Given : 

BC + XY = 18 units

Calculation : 

⇒ BC + XY = 18 units

We know XY = 1/2 BC

⇒ 1/2BC + BC = 18 

⇒ 3BC/2 = 18

⇒ BC = 12

Now XY = 6 

So BC - XY = 12 - 6 = 6

∴ The correct answer is 6cm.

Given:- 

AB = AD = 9 cm and AC = AE = 13 and BC = 15 cm

Concept Used:-

According to the concept of similarity, two triangles are
said to be similar if two sides of one triangle are in the
same ratio as two sides of the other triangle and the
the angle subtended by the two sides in both triangles is equal.

Calculation:-

Since AB = AD, and AC = AE,

By concept,

ΔABC ∼ ΔADE

Therefore,

⇒ AB/AD = BC/ED = AC/AE

Now,

⇒ AB/AD = BC/ED

⇒ 1 = 15/ED (∵ AB = AD)

⇒ ED = 15

∴ The length of ED is 15 cm.

Given:

∆ABC ~ ∆DEF, and BC = 4 cm, EF = 5 cm and the area of triangle ABC = 80 cm².

Concept used:

In two similar triangles, 

Ratio of their area is equal to ratio of the squares of their corresponding sides.

Calculations:

According to the question,

Area of ∆ABC : Area of ∆DEF = BC² : EF²

⇒80 : Area of ∆DEF = 4² : 5²

⇒Area of ∆DEF = 25 × 80/16

⇒Area of ∆DEF = 125

Hence, The Required value is 125 cm².

Given:

∠ABC = (x + 60)°

∠PQR = (85 - 4x)°

∠RPQ = (3x + 65)°

Calculation:

If ΔABC ≅ ΔPQR 

then ∠ABC = ∠PQR 

⇒ (x + 60) = (85 - 4x)

⇒ 5x = 85 - 60 

⇒ x = 25/5 = 5 units

So,

∠ABC = (x + 60)°

⇒ (5 + 60)° = 65°

∴ The correct answer is 65°.

Given:

In triangles ABD and FEC:

∠BAD = 60°

|BD| = |EC|

∠ABD = ∠FEC = 90°

|AB| = |FE|

Formula Used:

Trigonometric ratios (sine, cosine, tangent)

Calculations:

Consider triangle ABD:

∠BAD = 60°

∠ABD = 90°

Therefore, ∠ADB = 30° (since the sum of angles in a triangle is 180°)

Consider triangle FEC:

∠FEC = 90°

∠FCE = 30° (since ∠ADB = ∠FEC as the triangles are congruent)

Therefore, ∠CFE = 60° (since the sum of angles in a triangle is 180°)

Therefore, the ratio of ∠BAD to ∠FCE is 60°/30° = 2:1

Hence, the correct answer is option (4).

Formula Used:

Criteria for triangle congruence:

• ASA (Angle-Side-Angle)
• SSS (Side-Side-Side)
• SAS (Side-Angle-Side)
• AAS (Angle-Angle-Side)

Calculation:

Checking the given options:

1. ASA (Angle-Side-Angle) - Valid

2. AAS (Angle-Angle-Side) - Not a given option but valid for congruence

3. SSS (Side-Side-Side) - Valid

4. SAS (Side-Angle-Side) - Valid

5. AAA (Angle-Angle-Angle) - Not valid for congruence as it does not ensure congruence, only similarity

The correct answer is option 2 (angle-angle-angle).

Given:

In a ΔABC, if ∠A = 90°, AC = 5 cm, BC = 9 cm, and in ΔPQR, ∠P = 90°, PR = 3 cm, QR = 8 cm.

Calculation:

If ΔABC \(\cong\) ΔPQR, then 

AC = PR , BC = QR और AB = PQ

But,

AC ≠ PR , BC ≠ QR and AB ≠ PQ 

So they are not congruent.

So, ΔABC \(\ncong\) ΔPQR

∴ The correct option is 2

Given:

AD = x + 3, DB = 2x − 3, AE = x + 1 and EC = 2x − 2

Concept used:

When two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.

Calculation:

 

 

As DE ΙΙ BC, and ∠A is common in both triangle ABC and triangle ADE

So, ABC ∼ ADE

So,

AB/AD = AC/AE

⇒ (x + 3 + 2x - 3)/(x + 3) = (x + 1 + 2x - 2)/(x + 1)

⇒ (3x)/(x + 3) = (3x - 1)/(x + 1)

⇒ 3x² + 3x = 3x² - x + 9x - 3

⇒ 3x = 8x - 3

⇒ 5x = 3

⇒ x = 3/5

∴ The value of x is \({{3} \over 5}\).

Given:

ΔABC ~ ΔPQR 

PR = 5 cm and BC = 13 cm

Concept:

The ratio of the sides of two similar triangles is equal.

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure

Calculation

Since the triangles are congruent their corresponding angles and side will always be equal.

∴ The length of AB is 12 cm.

Given:

Two triangles are  ΔABC and ΔDEF

Concept used:

For congruent triangles, the perimeter of the triangles are always equal.

Calculation:

Among the given options,

Perimeter of ΔABC = Perimeter of ΔDEF

∴ The correct option is 2