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This mock test of Test: Properties Of Isosceles Triangle for Class 9 helps you for every Class 9 entrance exam.
This contains 10 Multiple Choice Questions for Class 9 Test: Properties Of Isosceles Triangle (mcq) to study with solutions a complete question bank.
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QUESTION: 1

In two right triangles, one side and an acute angle of one are equal to the corresponding side and angle of the other, then ΔABC ≅ ΔDEF by the criterion

Solution:
Answer is B because in this it is given that angle A = D . Then also B=E as they are right angle. And finally line CB = line FE (given) there for the criteria is AAS.

QUESTION: 2

In ΔABC if ∠A = ∠B, then

Solution:
Becuase Sides opposite to equal angles are also equal.angle A = angle BBC is opposite to angle A and AC is opposite to angle B.Therefore, AC=BC in triangle ABC.

QUESTION: 3

In the given figure, AB = AC and ∠ACD = 105°, ∠BAC will be

Solution:
Angle acb = 75 ( linear pair) Ab= Ac hence angle B= angle c in triangle ABC angle a+B+c= 180. angle B+ c = 150 hence angle c a= 30

QUESTION: 4

PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. then

Solution:

QUESTION: 5

The altitude of an equilateral triangle of side a to any of its other sides from the opposite vertex is

Solution:

QUESTION: 6

In an isosceles right angled triangle, the measures of the acute angles are

Solution:

QUESTION: 7

In ΔABC if AB = BC then:

Solution:

QUESTION: 8

Pick out the incorrect statement

Solution:

QUESTION: 9

If the bisector of the exterior vertical angle of a triangle is parallel to the base, then it is

Solution:

∠CAE is the external vertical angle and AD is its bisector.

∴ ∠CAD = ∠DAE .... (i)

As, AD || BC

∴ ∠CAD = ∠ACB .... (ii) (alternate angle)

and ∠DAE = ∠ABC ....(iii) (corresponding angle)

From (i), (ii) and (iii),

∠ABC = ∠ACB

∴ AC = AB (opposite sides to equal angles)

Hence, ΔABC is isosceles.

QUESTION: 10

In PQR, PQ = PR and R = 65°, then P = ?

Solution:

By using the theorem,If two sides of a triangle are equal then the opposite angles to the sides are equal.

⇒ if PQ=PR then ∠Q=∠R

in triangle PQR,

⇒ ∠P+∠Q+∠R=180°

⇒ ∠P+∠Q+∠Q=180° (∵∠Q=∠R)

⇒ ∠P+65°+65°=180°

⇒ ∠P+130°=180°

⇒ ∠P=180°-130°

⇒ ∠P=50

### Isosceles Triangle and its Properties

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### Examples: Equilateral and Isosceles Triangle

Video | 06:27 min

### Constructing a right isosceles triangle

Video | 01:26 min

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