Question

Class 7 Maths MCQ Questions for Congruence of Triangles with Answers?

Answer 1

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Practice MCQ Questions for Class 7 Maths

1. Under a given correspondence, two triangles are congruent if the three sides of the one are equal to the three corresponding sides of the other.’ The above is known as

(a) SSS congruence of two triangles
(b) SAS congruence of two triangles
(c) ASA congruence of two triangles
(d) RHS congruence of two right-angled triangles

2. Two triangles are congruent if two angles and the side included between them in one triangle is equal to the two angles and the side included between them of the other triangle. This is known

(a) RHS congruence criterion
(b) ASA congruence criterion
(c) SAS congruence criterion
(d) SSS congruence criterion

3. The symbol for congruence is

(a) ≡
(b) ≅
(c) ↔
(d) =

4. If △ABC≅△PQR, then which of the following is not true?

(a) BC=PQ
(b) AC=PR
(c) QR=BC
(d) AB=PQ

5. If ∆ ABC = ∆ PQR, then ∠B corresponds to

(a) ∠P
(b) ∠Q
(c) ∠R
(d) none of these

6. You want to show that ΔART≅ΔPEN If it is given that ∠T=∠N and you are to use SAS criterion, you need to have RT =

(a) EN
(b) AT
(c) EP
(d) none of these

7. Which congruence criterion do you use in the following?

Given AC = DF AB = DE BC = EF So, ∆ ABC ≅ ∆ DEF

(a) SSS
(b) SAS
(c) ASA
(d) RHS

8. In the following figure, the two triangles are congruent. The corresponding parts are marked. We can write ∆ RAT =?

(a) ∆ WON
(b) ∆ WNO
(c) ∆ OWN
(d) ∆ ONW

9. Complete the congruence statement ∆ QRS

(a) ∆ TPQ
(b) ∆ TQP
(c) ∆ QTP
(d) ∆ QPT

10. If ∆ ABC and ∆ PQR are to be congruent, name one additional pair of corresponding parts

(a) BC = QR
(b) BC = PQ
(c) BC = PR
(d) none of these

11. By which congruence, is ∆ ABC = ∆ FED?

(a) SSS
(b) SAS
(c) ASA
(d) RHS

12. Number of elements of a triangle is:

(a) 2
(b) 3
(c) 4
(d) 6

13. Two figures are said to be congruent if they have exactly the same:

(a) length and width
(b) shape and size
(c) area
(d) perimeter

14. One of the angles of a triangle is 50º and the other two angles are equal. Find the measure of each of the equal angles.

(a) 65º, 65º
(b) 50º,50º
(c) 45º,45º
(d) 65º,50º

15. ΔABC is right triangle in which ∠A = 90º and AB = AC. The values of ∠B and ∠C will be

(a) ∠B = ∠C = 30º
(b) ∠B = ∠C = 50º
(c) ∠B = ∠C = 45º
(d) ∠B = ∠C = 60º

16. Two students drew a line segment each. What is the condition for them to be congruent?

(a) They should be drawn with a scale
(b) They should be drawn on the same sheet of paper
(c) They should have different lengths
(d) They should have the same length

17. A triangle in which all three sides are of equal lengths is called __________.

(a) Isosceles
(b) Equilateral
(c) Scalene
(d) None of these

18. If the vertical angle of an isosceles triangle is 40°, then a measure of other two angles will be

(a) 60º, 60º
(b) 80º, 80º
(c) 70º, 70º
(d) 45º, 45º

19. Look at this series: 2, 4, 6, 8, 10, . . . What number should come next?

(a) 11
(b) 12
(c) 13
(d) 14

20. Which of the following examines the congruence of plane figures?

(a) Trial and error method
(b) Superposition method
(c) Substitution method
(d) Transposition method

21. In the given figure, say congruency of two triangles.

(a) ΔAOC ∪ ΔBOD
(b) ΔAOC ≠ ΔBOD
(c) ΔAOC ∪ ΔOBD
(d) none of these

22. The angles of a triangle are in the ratio 2:3:5 . What is the largest angle of the triangle?

(a) 54º
(b) 36º
(c) 90º
(d) 100º

23. What is the perimeter of the rectangle whose length is 40cm & a diagonal is 41cm?

(a) 164cm
(b) 162 cm
(c) 81 cm 
(d) 98 cm

24.  In the quadrilateral ABCD, AC = AD and AB bisect ∠A and ΔABC ≅ ΔABD. The relation between BC and BD is

(a) BC < BD
(b) BC > BD
(c) BC = BD
(d) None of these

25. How many altitudes can a triangle have?

(a) 1
(b) 2
(c) 3
(d) 4

Answer 2

1. Answer: (a) SSS congruence of two triangles

Explanation: SSS congruence of two triangles: Under a given correspondence, two triangles are congruent if the three sides of the one triangle are equal to the three corresponding sides of the other triangle and this is called SSS congruence condition.

2. Answer: (b) ASA congruence criterion

Explanation: When two angles and side included in between these angles of one triangle are same as another one, both these triangle are Congruent.This criteria of congruency is knows as ASA criterion as a side included between two angles are all same.

3. Answer: (b) ≅

Explanation:  A symbol commonly used for congruence is an equals symbol with a tilde above it, ≅, corresponding to the Unicode character 'approximately equal to'.

4. Answer: (a) BC=PQ

Explanation:  Given, ABC≅PQR

Thus.corresponding sides are equal.

Hence, AB=PQ 

AC=PR

BC=QR

Hence, BC=PQ is not true for the triangles.

5. Answer: (b) ∠Q

Explanation:  ∆ ABC = ∆ PQR

Then

∠A=∠P

∠B=∠Q

∠C=∠R

6. Answer: (a) EN

Explanation: Given that ΔART≅ΔPEN and ∠T=∠N

If the SAS (side angle side) criterion is used, then corresponding sides which are adjacent the equivalent angle of the triangle are equivalent. Therefore, RT=EN and PN=AT

7. Answer: (a) SSS

Explanation: Since all sides of ΔABC are equal to all corresponding sides of ΔDEF So, we will use SSS congruence criterion to prove ΔABC≅ΔDEF.

8. Answer: (a) ∆ WON

Explanation: In the figure, given two triangles are congruent. So, the corresponding parts are:  A ↔ O, R ↔ W, T ↔ N. We can write,  Δ  RAT ≅  Δ  WON [By SAS congruence rule].

9. Answer: (a) ∆ TPQ

Explanation: In the given figure,

QR=TP

QS=TQ

RS=PQ

∠P=∠R

⟹ △QRS≅△TPQ    (by SSS congruence)

∴ we get the following correspondence in the vertices

Q↔T

R↔P

S↔Q

Hence, △QRS≅△TPQ

10. Answer: (a) BC = QR

Explanation: 

The additional corresponding part is BC = RQ by ASA congruence rules.

11. Answer: (c) ASA

Explanation:  ∠B = ∠E, BC = ED, 

∠D = ∠C (By angle sum property of a triangle).

12. Answer: (d) 6

Explanation: A triangle has total six elements. They are its three angles and three sides.

13. Answer: (b) shape and size

Explanation: Two plane figures are congruent to each other, if trace copy of one of the figures covers the other figure completely.

14. Answer: (a) 65º, 65º

Explanation: Let the equal angles be x,x

Then by angle property:

x + x + 50º = 180º

2x = 130º

x = 130º/2

x = 65º

Angles are 65º, 65º

15. Answer: (c) ∠B = ∠C = 45º

Explanation: Since AB=AC, 

So, △ABC is Right-angled isosceles.

∠B=∠C ..........(angles opp. to equal sides are equal)

∠A+∠B+∠C=180º ...(angle - sum property of a triangle)

Substituting ∠B =∠C, ∠A = 90º

90º + 2∠B = 180º

2∠B = 180º–90º = 90º

∠B = 45º

∠B = ∠C = 45º

16. Answer: (d) They should have the same length

Explanation: The condition for the line segments to be congruent is that they should have the same length.

17. Answer: (b) Equilateral

Explanation:  A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides and angles equal.

18. Answer: (c) 70º, 70º

Explanation:  Let the base angles be  ′x ′

Therefore

x+x+40º = 180º

2x = 180º - 40º

2x = 140º

x = 70º

Hence,  The base angles of the triangle are 70º, 70º

19. Answer: (b) 12

Explanation:  This is a simple addition series.

Each number increases by 2.

Like -

First number is 2

Second number = 2 + 2 =4

Third number = 4 + 2 = 6

Fourth number = 6 + 2 = 8

Fifth number = 8 + 2 = 10  and

Sixth number = 10 + 2 = 12

Hence, The answer is (b) 12.

Answer 3

20. Answer: (b) Superposition method

Explanation:  The method of superposition examines the congruence of plane figures, line segments and angles. Two plane figures are congruent if each, when superimposed on the other, covers it exactly. Congruence is denoted by the symbol '≅'.

21. Answer: (a) ΔAOC ∪ ΔBOD

Explanation: ∠AOC = ∠BOD = 30°. Vertically opposite angles. according to ASA congruency two triangles are congruent.

22. Answer: (c) 90º

Explanation:  Let the angles of a triangle be 2x,3x,5x.

Sum of interior angles of a triangle is 180º

Hence ∠A+∠B+∠C = 180º

2x+3x+5x = 180º

10x = 180º

x = 18º

∴ Angles are 36º , 54º , 90º

The largest angle of the triangle 90º

23. Answer: (d) 98 cm

Explanation:  Given that length of the side of the rectangle is l=40cm and

the length of the diagonal is d=41cm

let breadth be bcm

l² + b² = d²

40² + b² = 4l²

b² = 81

b = 9cm

we know that the perimeter of the rectangle is 2(l+b)

= 2(40+9)

= 98cm

24. Answer: (c) BC = BD

Explanation:  In △ABC and △ABD,

AC=AD

∠CAB=∠DAB

AB=AB

So, by SAS congruence rule,

△ABC≅△ABD

BC=BD........ [By CPCT]

25. Answer: (c) 3

Explanation:  The three altitudes of a triangle intersect at the orthocenter, which for an acute triangle is inside the triangle.

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