Question 16
In the given figure, PQ $⊥$ RQ, PQ = 5 cm and QR = 5 cm. Then, $△ P Q R$ is

a) a right-angled triangle but not isosceles
b) an isosceles right-angled triangle
c) isosceles but not a right-angled triangle
d) neither isosceles nor right-angled triangle

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Solution

Given : PQ $⊥$ RQ, PQ = 5 cm and QR = 5 cm

Since, PQ $⊥$ RQ

So, $∠$ PQR = $90^{\circ}$

$∴ △$ PQR is a right angled triangle.

Also, in $△$ PQR,

PQ = QR

$∴ △$ PQR is an isosceles triangle.

Hence, $△$ PQR is an isosceles right-angled triangle.

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Question 16
In the given figure, PQ $⊥$ RQ, PQ = 5 cm and QR = 5 cm. Then, $△ P Q R$ is

a) a right-angled triangle but not isosceles
b) an isosceles right-angled triangle
c) isosceles but not a right-angled triangle
d) neither isosceles nor right-angled triangle

Question 7

Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is

a) Obtuse-angled triangle
b) Acute angled triangle
c) Right angled triangle
d) An isosceles right triangle.

In $△$ ABC, ∠ABC = 90 $^{\circ}$ , AB = BC = 5 cm. What is this triangle called?

Q. The triangle formed by the common tangents to the parabola

y^{2} = 4 x

and the circle

x^{2} + y^{2} + 2 x = 0

Question 14

If in an isosceles triangle, each of the base angle is $40^{\circ}$ , then the triangle is

a) Right angled triangle
b) Acute angled triangle
c) Obtuse-angled triangle
d) Isosceles right-angled triangle

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Types of Triangles Based on Lengths of Sides

Standard VI Mathematics

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Question 16 In the given figure, PQ⊥RQ, PQ = 5 cm and QR = 5 cm. Then, △PQR is a) a right-angled triangle but not isosceles b) an isosceles right-angled triangle c) isosceles but not a right-angled triangle d) neither isosceles nor right-angled triangle

Given : PQ⊥RQ, PQ = 5 cm and QR = 5 cm Since, PQ⊥RQ So, ∠ PQR = 90∘ ∴△ PQR is a right angled triangle. Also, in △PQR, PQ = QR ∴△ PQR is an isosceles triangle. Hence, △ PQR is an isosceles right-angled triangle.

Question 16
In the given figure, PQ $⊥$ RQ, PQ = 5 cm and QR = 5 cm. Then, $△ P Q R$ is

a) a right-angled triangle but not isosceles
b) an isosceles right-angled triangle
c) isosceles but not a right-angled triangle
d) neither isosceles nor right-angled triangle

Given : PQ $⊥$ RQ, PQ = 5 cm and QR = 5 cm

Since, PQ $⊥$ RQ

So, $∠$ PQR = $90^{\circ}$

$∴ △$ PQR is a right angled triangle.

Also, in $△$ PQR,

PQ = QR

$∴ △$ PQR is an isosceles triangle.

Hence, $△$ PQR is an isosceles right-angled triangle.