Question

ΔPQR is constructed such that PQ = 5 cm, PR = 5 cm and ∠RPQ = 50°. Identify the type of triangle constructed. 

.An isosceles triangle
.An acute angled triangle
.An obtuse angled triangle
.Both [a] and [b]
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Answer 1

Answer :-

Given that :

ΔPQR is constructed such that PQ = 5cm, PR = 5cm and ∠RPQ = 50°

　　Here, PQ = PR = 5cm 　(Isosceles Triangle)

　　Also, ∠RPQ = 50° 　(Acute angle)

Required Answer :

Both (a) and (b) \Large\bf{✓}✓

Answer 2

The type of triangle constructed is an isosceles triangle and an acute-angled triangle (Option d)

Given

In ΔPQR, PQ = PR = 5cm

∠RPQ = 50°

To Find

The type of triangle constructed

Solution

Since PQ = PR in ΔPQR, angles opposite to equal sides, i.e., ∠PRQ and ∠PQR, are also equal to each other. Let us assume that angle is $a$.

The sum of all sides of a triangle is equal to 180°.

That is, ∠PRQ + ∠PQR +∠RQP = 180 -> $2a$ + 50 = 180

$2a$ = 130°

$a$ = 65°

Now since PQ = PR and the angles are not 60° each, the triangle is isosceles

Also, since all the angles of the triangle are less than 90°, the triangle is acute-angled.

Hence, the type of triangle constructed is an isosceles triangle and an acute-angled triangle.