Class 9 Practice – Level 3 – Set 1 – Triangles

Total questions: 15

△ABC is an isosceles triangle in which AB = AC. Sides BA is produced to D such that AD = AB. What is the value of ∠BCD?

Topic: Isosceles Triangle Properties

∠BCD = 60°

∠BCD = 90°

∠BCD = 180°

∠BCD = 150°

None

Find ∠ADC in the given figure

Topic: Angle Calculation in Triangle

75°

95°

85°

55°

None

In △ABC, BD ⊥ AC and CE ⊥ AB. If BD and CE intersect at O, then ∠BOC =

Topic: Intersection of Perpendiculars in a Triangle

∠A

90° + A

180° + ∠A

180° − ∠A

None

In the given figure, Y Z is parallel to MN, XY is parallel is LM and XZ is parallel to LN . Then MY is

Topic: Parallel Lines and Proportion

Median of △LMN

The angular bisector of ∠LMN

Perpendicular to LN

Perpendicular bisector of LN

None

In figure, AD and BE are medians of △ABC and BE∥DF. If the value of CF is equal to $ \displaystyle \dfrac{\text{k}}{4}\times \text{AC}$, then the value of k is

Topic: Median of a Triangle

None

In the given figure, x is a point in the interior of square ABCD. AXYZ is also a square. If DY = 3 cm and AZ = 2 cm, then BY =

Topic: Properties of Squares and Geometry

5 cm

6 cm

7 cm

8 cm

None

If the bisectors of the exterior vertical angle of a triangle be parallel to the base. Then the triangle is

Topic: Exterior Angle Property

scalene

equilateral

right angled

isosceles

None

If ABC is a triangle right angled at B and M, N are the mid-points of AB and BC, then 4($ \displaystyle \text{A}{{\text{N}}^{2}}+\text{C}{{\text{M}}^{2}}$) is equal to :

Topic: Right-Angled Triangle

$ \displaystyle 4\text{A}{{\text{C}}^{2}}$

$ \displaystyle 5\text{A}{{\text{C}}^{2}}$

$ \displaystyle \dfrac{5}{4}\text{A}{{\text{C}}^{2}}$

$ \displaystyle 6\text{A}{{\text{C}}^{2}}$

None

In △ABC, D is a point on BC such that 3BD = BC. If each side of the triangle is 12 cm. then AD equals

Topic: Distance Formula in Triangles

$ \displaystyle 4\sqrt{5}$

$ \displaystyle 4\sqrt{6}$

$ \displaystyle 4\sqrt{7}$

$ \displaystyle 4\sqrt{11}$

None

10.

If the line segment joining the midpoint of the consecutive side of quadrilateral ABCD form a rectangle then ABCD must be

Topic: Properties of Quadrilaterals

rhombus

square

kite

all of the above

None

11.

In the given figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that AD bisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is

Topic: Angle Bisector and Perpendicular

72°

73°

74°

95°

None

12.

In the figure given below, DE = GH, FE = FG, FD = FH and ∠EFH = 90°. When of the following congruency axiom is suitable to prove that △DEF ≅ △HGF ?

Topic: Congruence in Triangles

S.S.S.

S.A.S.

R.H.S.

All of the above

None

13.

In the following figure, ∠DAC = 30°, ∠ABC = ∠ADC = 95° and ∠BCA = 55°. If the area of △ACD is $ \displaystyle 30\text{ c}{{\text{m}}^{2}}$, what is the area of △ABC ?

Topic: Angle Properties in Triangles

$ \displaystyle 60\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 90\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 30\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 40\text{ c}{{\text{m}}^{2}}$

None

14.

In figure, AD = BC and BC = CA. Then,

Topic: Congruence in Triangles

∠ADB = ∠DAB

∠ADB = ∠BCA

∠ADB = ∠CBA

∠DAB = ∠BCA

None

15.

Consider the following statements relating to the congruency of two right triangles.

Topic: Congruence of Right-Angled Triangles

(1) Equality of two sides of one triangle with any two sides of the second makes the triangle congruent.
(2) Equality of the hypotenuse and a side of one triangle with the hypotenuse and a side of the second respectively makes the triangle congruent.
(3) Equality of the hypotenuse and an acute angle of one triangle with the hypotenuse and an angle of the second respectively makes the triangle congruent. Of these statements:

1,2 and 3 are correct

1 and 2 are correct

1 and 3 are correct

2 and 3 are correct

None

1 out of 15

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Class 9 Practice – Level 3 – Set 1 – Triangles

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