CBSE Class 7 Mathematics Congruence of Triangles Assignment Set A

Question. In ΔABC, AB = AC and AD is perpendicular to BC. State the property by which ΔADB ≅ ΔADC.
(A) S.A.S. property
(B) S.S.S. property
(C) R.H.S. property
(D) A.S.A. property
Answer : C

Question. 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
Answer : D

Question. In the given figure, if AD = BC and ADIIBC, which of the following is true?

(A) AB = AD
(B) AB = DC
(C) BC = CD
(D) AC = AD
Answer : B

Question. In ΔPQR and ΔXYZ, ∠P = 50°, XV = PQ, and XZ = PR. By which property are ΔXYZ and ΔPQR congruent?
(A) S.S.S. property
(B) S.A.S. property
(C) A.S.A. property
(D) R.H.S. property
Answer : B

Question. A: Two triangles are said to be congruent if two sides and an angle of one triangle are respectively equal to the two sides and an angle of the other.
R : Two triangles are congruent if two sides and the included angle of one are equal to the corresponding two sides and included angle of the other.
Given A & R, which of the following statements is correct?
(A) A is false and R is the correct explanation of A.
(B) A is true and R is the correct explanation of A.
(C) A is true and R is false.
(D) A is false and R is true.
Answer : A

Question. Two triangles, ΔPQR and ΔDEF are of the same size and shape. What can we conclude about them?
(A) ΔPQR is smaller than ΔDEF.
(B) ΔPQR is larger than ΔDEF.
(C) ΔPQR is congruent to ΔDEF .
(D) ΔPQR is not congruent to ΔDEF .
Answer : C

Question. Which of the following examines the congruence of plane figures?
(A) Trial and error method
(B) Superposition method
(C) Substitution method
(D) Transposition method
Answer : B

Question. 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.
Answer : C

Question. In ΔABC and ΔPQR, AB = x cm, BC = y cm and CA = z cm. What are the measures of sides PQ, QR and RP of ΔPQR if ΔABC ≅ ΔABC ≅ ΔPQR

Answer : A

(a - b): In the given figure, AD = CD and AB = CB

Question a. What are the three pairs of equal parts?
(A) ∠ADB = ∠CDB, ∠ABD = ∠CBD; BD = BD
(B) AD = AB, DC = CB, BD = BD
(C) AB = CD, AD = BC, BD = BD
(D) ∠ADB = ∠CDB, ∠ABD = ∠CBD; ∠DAB = ∠DBC
Answer : A

Question b. Which of the following is the correct conclusion?
(A) ΔABC and ΔCBD are isosceles triangles.
(B) BD bisects ∠ADC .
(C) BD bisects ∠BAD .
(D) ΔABC and ΔCBD are equilateral triangles.
Answer : B

Question. In the given figure, AB = AC and AD is the bisector of ∠BAC.

Which among the following statements is true?
(A) ΔADB ≅ ΔAB C
(B) ΔADC ≅ ΔABC
(C) ∠B = ∠C
(D) ∠ABC = ∠CAB
Answer : C

Question. In ΔABC and ΔDEF, AC = OF, AB = DE and BC = EF. By which property are ΔABC and ΔDEF congruent?
(A) R.H.S. property
(B) S.S.S. property
(C) S.A.S. property
(D) A.S.A. property
Answer : B

Question. For the triangles ΔART and ΔPEN given, if S.A.S. criterion sho uld be used given ∠T = ∠N , what are the respective measures of PN and RT?

(A) TR and PE
(C) AT and EN
(B) AR and PE
(D) AR and PN
Answer : C

Question. Which of the following is an example of A.S.A. criterion of congruency for two triangles ∠AD B and ∠DEF?
(A) A B = EF, ∠B = ∠E and ∠C = ∠F
(B) BC = EF, ∠B = ∠E and ∠C = ∠F
(C) AC = EF, ∠B = ∠D and ∠C = ∠F
(D) AC = DE , ∠B = ∠D and ∠C = ∠F
Answer : B

Question. In the figure given, AC = BD and ∠BAC = ∠CDB = 90°.

If ΔABC ≅ Δ DCB by R.H.S. property which of the following is required?
(A) The measure of AB.
(B) The measure of CD.
(C) The m easure of BC.
(D) AC = BD
Answer : C

Question. Which of the following criterion does not exist?
(A) A.S.A. criterion
(B) R.H.S. criterion
(C) A.A.A. criterion
(D) S.S.S. criterion
Answer : C

Question. In two triangles, the three angles of one triangle are correspond ingly 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.
Answer : A

(a - b): ΔABC is congruent to ΔPQR under thecorrespondence ABC ↔ RQP.

Question a. Which part corresponds to PQ ?
(A) C B
(B) A C
(C) Q R
(D) A B
Answer : A

Question b. Which part of ΔABC corresponds to RP ?
(A) AB
(B) AC
(C) CA
(D) BC
Answer : B

Question. ΔABC is congruent to ΔXYZ. Find the measures of ∠x and ∠y respectively.

(A) 80°, 60°
(C) 80°, 40°
(B) 60°, 40°
(D) 60°, 80°
Answer : A

Question. ΔABC ≅ ΔDEF,and AB = 3 em, EF = 8 em and OF = 10 em. What are the respective lengths of AC and DE in em?
(A) 10,3
(B) 10,8
(C) 8,3
(D) 3,10
Answer : A

Question. ΔABC = ΔFOE What is the measure of ∠F?

(A) 70°
(B) 50°
(C) 130°
(D) 60°
Answer : A

Question. In the figure, PQ = PS and QR = SR. If ΔPQR is congruent to ΔPSR, which of the following is correct?

(A) ∠QPR = ∠PRS
(B) ∠RPS = ∠RQP
(C) ∠QRP = ∠SRP
(D) PR = RS
Answer : C

Question. Identify the incorrect statement.
(A) The corresponding sides of congruent triangles are equal.
(B) The corresponding angles of congruent triangles are equal.
(C) Two triangles cannot be congruent.
(D) There are four congruency conditions for congruence of triangles.
Answer : C

Q1. Define congruence of triangles.

Q2. Write criteria of congruence of a triangle.

Q3. Which congruence criteria do you use in the above figure.

AB = PQ ; Angle B = Angle Q ; BC = QR

Q 4.Give any three real life example for congruent shape.

Q5. AB = 5 cm ; angle B = 50⁰ ; BC = 5.5 cm ; & DF = 5 cm angle F = 50⁰

& FE = 5.5 cm , then write the triangles in order they are congruent & Write also criteria.

Q6. In the figure , AB = AC & AD is the bisector of angle BAC.

i) State three pairs of equal parts in triangles ADB & ADC.

ii) Is triangle ADB is congruent to triangle ADC .

Q 7. Which angle is included between DE & EF of triangle DEF?

Q 8.In a squared sheet , draw two triangles of equal areas such that

i) the triangle are congruent .

ii) the triangles are not congruent .

What can you say about their perimeter ?

Q9. If AC = DC ; angle ABC = angle DBC & BC = BC STATE THE CRITERIA OF THE CONGRUENCE.

Q10. If DA is perpendicular to AB & CB is perpendicular to BA & AC = BD Then state which two triangle are congruent & by which criteria.

Please click the link below to download CBSE Class 7 Mathematics Congruence of Triangles Assignment Set A