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THE TRIANGLE AND ITS PROPERTIES

298351 If $△ ABC$ and $△ DBC$ are on the same base BC, AB = DC and AC = DB (figure). then which of the following gives a congruence relationship?
0

1

△ ABC ≅ △ DBC

2

△ ABC ≅ △ CBD

3

△ ABC ≅ △ DCB

4

△ ABC ≅ △ BCD

Explanation:

$△ ABC ≅ △ DCB$
Since, AB = DC [given]
and AC = DB [common base]
BC = BC
By SSS congruence criterion, $△ ABC ≅ △ DCB$

THE TRIANGLE AND ITS PROPERTIES

298352 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): All sides of a triangle are 8cm. It is a equilateral Triangle.
Reason (R): Equilateral Triangles have all 3 sides equal.

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true but R is not the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

THE TRIANGLE AND ITS PROPERTIES

298353 In Figure. PB = PD. The value of x is:1

1 85°

2 90°

3 25°

4 35°

Explanation:

25°
$In △ PBD,$ $∠ 1 + 120^{\circ} = 180^{\circ}$ $[linear pair]$
$∠ 1 = 180^{\circ} - 120^{\circ} = 60^{\circ}$
Also, $∠ 1 = ∠ 2 = 60^{\circ}$ $[∵ PB = PD]$
2
Also, $∠ 2 + ∠ 3 = 180^{\circ}$ $[linear pair]$
$\Rightarrow 60^{\circ} + ∠ 3 = 180^{\circ} \Rightarrow ∠ 3 = 180^{\circ} - 60^{\circ}$
$\Rightarrow ∠ 3 = 120^{\circ}$
$In △ PDC,$ $35^{\circ} + ∠ 3 + x^{\circ} = 180^{\circ}$ [angle sum property of a triangle]
$\Rightarrow 35^{\circ} + 120^{\circ} + x^{\circ} = 180^{\circ}$
$\Rightarrow 155^{\circ} + x^{\circ} = 180^{\circ} \Rightarrow x^{\circ} = 180^{\circ} - 155^{\circ}$
$\Rightarrow x = 25^{\circ}$

THE TRIANGLE AND ITS PROPERTIES

298354 The sum of the lengths of any two sides of a triangle is _____________ the third side of the triangle.

1 Greater than

2 Half

3 Less than

4 Double

THE TRIANGLE AND ITS PROPERTIES

298351 If $△ ABC$ and $△ DBC$ are on the same base BC, AB = DC and AC = DB (figure). then which of the following gives a congruence relationship?
0

1

△ ABC ≅ △ DBC

2

△ ABC ≅ △ CBD

3

△ ABC ≅ △ DCB

4

△ ABC ≅ △ BCD

Explanation:

$△ ABC ≅ △ DCB$
Since, AB = DC [given]
and AC = DB [common base]
BC = BC
By SSS congruence criterion, $△ ABC ≅ △ DCB$

THE TRIANGLE AND ITS PROPERTIES

298352 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): All sides of a triangle are 8cm. It is a equilateral Triangle.
Reason (R): Equilateral Triangles have all 3 sides equal.

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true but R is not the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

THE TRIANGLE AND ITS PROPERTIES

298353 In Figure. PB = PD. The value of x is:1

1 85°

2 90°

3 25°

4 35°

Explanation:

25°
$In △ PBD,$ $∠ 1 + 120^{\circ} = 180^{\circ}$ $[linear pair]$
$∠ 1 = 180^{\circ} - 120^{\circ} = 60^{\circ}$
Also, $∠ 1 = ∠ 2 = 60^{\circ}$ $[∵ PB = PD]$
2
Also, $∠ 2 + ∠ 3 = 180^{\circ}$ $[linear pair]$
$\Rightarrow 60^{\circ} + ∠ 3 = 180^{\circ} \Rightarrow ∠ 3 = 180^{\circ} - 60^{\circ}$
$\Rightarrow ∠ 3 = 120^{\circ}$
$In △ PDC,$ $35^{\circ} + ∠ 3 + x^{\circ} = 180^{\circ}$ [angle sum property of a triangle]
$\Rightarrow 35^{\circ} + 120^{\circ} + x^{\circ} = 180^{\circ}$
$\Rightarrow 155^{\circ} + x^{\circ} = 180^{\circ} \Rightarrow x^{\circ} = 180^{\circ} - 155^{\circ}$
$\Rightarrow x = 25^{\circ}$

THE TRIANGLE AND ITS PROPERTIES

298354 The sum of the lengths of any two sides of a triangle is _____________ the third side of the triangle.

1 Greater than

2 Half

3 Less than

4 Double

THE TRIANGLE AND ITS PROPERTIES

298351 If $△ ABC$ and $△ DBC$ are on the same base BC, AB = DC and AC = DB (figure). then which of the following gives a congruence relationship?
0

1

△ ABC ≅ △ DBC

2

△ ABC ≅ △ CBD

3

△ ABC ≅ △ DCB

4

△ ABC ≅ △ BCD

Explanation:

$△ ABC ≅ △ DCB$
Since, AB = DC [given]
and AC = DB [common base]
BC = BC
By SSS congruence criterion, $△ ABC ≅ △ DCB$

THE TRIANGLE AND ITS PROPERTIES

298352 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): All sides of a triangle are 8cm. It is a equilateral Triangle.
Reason (R): Equilateral Triangles have all 3 sides equal.

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true but R is not the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

THE TRIANGLE AND ITS PROPERTIES

298353 In Figure. PB = PD. The value of x is:1

1 85°

2 90°

3 25°

4 35°

Explanation:

25°
$In △ PBD,$ $∠ 1 + 120^{\circ} = 180^{\circ}$ $[linear pair]$
$∠ 1 = 180^{\circ} - 120^{\circ} = 60^{\circ}$
Also, $∠ 1 = ∠ 2 = 60^{\circ}$ $[∵ PB = PD]$
2
Also, $∠ 2 + ∠ 3 = 180^{\circ}$ $[linear pair]$
$\Rightarrow 60^{\circ} + ∠ 3 = 180^{\circ} \Rightarrow ∠ 3 = 180^{\circ} - 60^{\circ}$
$\Rightarrow ∠ 3 = 120^{\circ}$
$In △ PDC,$ $35^{\circ} + ∠ 3 + x^{\circ} = 180^{\circ}$ [angle sum property of a triangle]
$\Rightarrow 35^{\circ} + 120^{\circ} + x^{\circ} = 180^{\circ}$
$\Rightarrow 155^{\circ} + x^{\circ} = 180^{\circ} \Rightarrow x^{\circ} = 180^{\circ} - 155^{\circ}$
$\Rightarrow x = 25^{\circ}$

THE TRIANGLE AND ITS PROPERTIES

298354 The sum of the lengths of any two sides of a triangle is _____________ the third side of the triangle.

1 Greater than

2 Half

3 Less than

4 Double

THE TRIANGLE AND ITS PROPERTIES

298351 If $△ ABC$ and $△ DBC$ are on the same base BC, AB = DC and AC = DB (figure). then which of the following gives a congruence relationship?
0

1

△ ABC ≅ △ DBC

2

△ ABC ≅ △ CBD

3

△ ABC ≅ △ DCB

4

△ ABC ≅ △ BCD

Explanation:

$△ ABC ≅ △ DCB$
Since, AB = DC [given]
and AC = DB [common base]
BC = BC
By SSS congruence criterion, $△ ABC ≅ △ DCB$

THE TRIANGLE AND ITS PROPERTIES

298352 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): All sides of a triangle are 8cm. It is a equilateral Triangle.
Reason (R): Equilateral Triangles have all 3 sides equal.

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true but R is not the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

THE TRIANGLE AND ITS PROPERTIES

298353 In Figure. PB = PD. The value of x is:1

1 85°

2 90°

3 25°

4 35°

Explanation:

25°
$In △ PBD,$ $∠ 1 + 120^{\circ} = 180^{\circ}$ $[linear pair]$
$∠ 1 = 180^{\circ} - 120^{\circ} = 60^{\circ}$
Also, $∠ 1 = ∠ 2 = 60^{\circ}$ $[∵ PB = PD]$
2
Also, $∠ 2 + ∠ 3 = 180^{\circ}$ $[linear pair]$
$\Rightarrow 60^{\circ} + ∠ 3 = 180^{\circ} \Rightarrow ∠ 3 = 180^{\circ} - 60^{\circ}$
$\Rightarrow ∠ 3 = 120^{\circ}$
$In △ PDC,$ $35^{\circ} + ∠ 3 + x^{\circ} = 180^{\circ}$ [angle sum property of a triangle]
$\Rightarrow 35^{\circ} + 120^{\circ} + x^{\circ} = 180^{\circ}$
$\Rightarrow 155^{\circ} + x^{\circ} = 180^{\circ} \Rightarrow x^{\circ} = 180^{\circ} - 155^{\circ}$
$\Rightarrow x = 25^{\circ}$

THE TRIANGLE AND ITS PROPERTIES

298354 The sum of the lengths of any two sides of a triangle is _____________ the third side of the triangle.

1 Greater than

2 Half

3 Less than

4 Double