Congruence of Triangles Test

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Congruence of Triangles Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

If for ΔABCand ΔDEF,the correspondence CAB↔EDFgives a congruence, then which of the following is NOT true?

A
AC=DE

B
AB=EF

C
∠A=∠D

D
∠C=∠E

Solution

We can conclude CA= ED, AB= DF, CB = EF, ∠CAB=∠EDF, ∠ACB=∠DEF, ∠ABC=∠DFE
Question 2
1 / -0

ΔABC≅ΔFDEand AB=3 cm, EF=8 cmand DF=10 cm. What are the respective lengths of AC and DE in cm?

A
10, 3

B
10, 8

C
8, 3

D
3, 10

Solution

The sides corresponding to AC and DE respectively are DF and AB. ∴ AC=10 cm,and DE=3 cm.
Question 3
1 / -0

Which of the following is a pair of congruent figures?

A
A regular pentagon and a regular hexagon.

B
A rhombus and a square.

C
Two equilateral triangles of the same length of their sides.

D
A quadrilateral and a rectangle.

Solution

Two equilateral triangles of the same length of their sides are congruent
Question 4
1 / -0

In two triangles, the three angles of one triangle are correspondingly equal to three angles of another triangle. Which of the following is a correct statement?

A
One triangle is an enlarged copy of other.

B
The two triangles are necessarily congruent.

C
The two triangles are congruent by A.A.A. congruency criterion.

D
All of the above.

Solution

If the three angles of a triangle are congruent to corresponding angles of the other, it is an enlarged copy of the triangle.
Question 5
1 / -0

In the given figure, ABC is an isosceles triangle in whichAB=AC. If E and F be the midpoints of AC and AB respectively, then BE is equal to ____.

A
CF

B
AB

C
CE

D
BF

Solution

Since, AB = AC ⇒ 1/2AB=1/2AC ⇒ BF=EC Also. AB=AC ⇒ ∠B=∠C [Angles opposite to equal sides are equal] In Δ BECand Δ CFB EC = FB (proved above) ∠B=∠C (proved above) BC = BC (common) ∴ ΔBEC≅ΔCFB (By SAS) ⇒ BE=CF (By CPCT)
Question 6
1 / -0

Which of the following statements is CORRECT?

A
In an isosceles triangle, the angles opposite to equal sides are equal.

B
The bisector of the vertical angle of an isosceles triangle bisects the base at right angles.

C
If the hypotenuse and an acute angle of one right angled triangle is equal to the hypotenuse and the corresponding acute angle of another triangle, then the triangles are congruent.

D
All of these

Solution

All of the statements are correct

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Congruence of Triangles Test - 7

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Congruence of Triangles Test - 7

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Question 1

AC=DE

AB=EF

∠A=∠D

∠C=∠E

Solution

Question 2

10, 3

10, 8

8, 3

3, 10

Solution

Question 3

A regular pentagon and a regular hexagon.

A rhombus and a square.

Two equilateral triangles of the same length of their sides.

A quadrilateral and a rectangle.

Solution

Question 4

One triangle is an enlarged copy of other.

The two triangles are necessarily congruent.

The two triangles are congruent by A.A.A. congruency criterion.

All of the above.

Solution

Question 5

CF

AB

CE

BF

Solution

Question 6

In an isosceles triangle, the angles opposite to equal sides are equal.

The bisector of the vertical angle of an isosceles triangle bisects the base at right angles.

If the hypotenuse and an acute angle of one right angled triangle is equal to the hypotenuse and the corresponding acute angle of another triangle, then the triangles are congruent.

All of these

Solution

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