Geometric Twins Class 7 Worksheet with Answers Maths Chapter 1

Teachers can assign these Class 7 Ganita Prakash Worksheet and NCERT Class 7 Maths Chapter 1 Geometric Twins Worksheet with Answers Pdf for daily practice.

Geometric Twins Worksheet Class 7

Class 7 Maths Geometric Twins Worksheet

Worksheet On Geometric Twins Class 7 – Geometric Twins Class 7 Ganita Prakash Worksheet

Multiple Choice Questions

Question 1.
Which of the following is not a criterion for congruence of triangles?
(a) SAS
(b) ASA
(c) SSA
(d) SSS
Answer:
(c) SSA

Question 2.
Which congruence criterion do you use in the following case?
Given,
ZX = RP,
RQ = ZY,
∆PRQ = ∆XZY.
So, APQR s AXYZ.
(a) ASA rule
(b) SSS rule
(c) RHS rule
(d) SAS rule
Answer:
(d) SAS rule

Question 3.
In the given figure, AF = CD and ∠AFE = ∠CDE. If EF = 5 cm then ED is equal to

(a) 6 cm
(b) 5 cm
(c) 8 cm
(d) 10 cm
Answer:
(b) 5 cm

Question 4.
In the given figure, if PM = QM, ∠SMP = ∠RMQ and ∠RPQ = ∠SQM. Therefore, ∆PMR = ∆QMS by which congruence rule?

(a) SSS
(b) SAS
(c) ASA
(d) None of these
Answer:
(c) ASA

(v) In ∆ABC, if BC = AB and ∠B = 80° then ∠A is equal to
(a) 80°
(b) 40°
(c) 50°
(D) 100°
Answer:
(c) 50°

Assertion and Reason-based Questions.

1. Assertion (A) In ∆ABC and ∆PQR, if ∠A = 30°, ∠C = 70°, AB = 5 cm, ∠P = 30°,
∠R = 70° and QR = 5 cm then ∆ABC = ∆PQR.
Reason (R) If three sides of one triangle are equal to the three corresponding sides of another triangle then the two triangles are congruent.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(b) Both A and R are true but R is not the correct explanation of A.

2. Assertion (A) In ∆ABC, if AB = AC and ∠C = 48° then ∠A – 64°.
Reason (R) Angles opposite to equal side of an isosceles triangle are equal.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(d) A is false but R is true.

Fill in the blanks

1. Two triangles are said to be congruent, if pairs of corresponding sides and the corresponding ______ are equal.
Answer:
angle

2. When the hypotenuse and one side of one right-angled triangle are respectively equal
to the hypotenuse and one side of the other right-angled triangle, the triangles are congruent. This is called ______ congruence of triangles.
Answer:
RHS

3. If two angles and the non-included side of one triangle are respectively equal to the two angles and the non-included side of the other triangle then the triangles are congruent by ______ congruence criterion.
Answer:
AAS

4. In ∆ABC, if AB = AC and ∠B = 40° then find ∠A.
Answer:
100°

State whether the statements given below are True or False.

1. If three sides of a triangle are equal to the corresponding sides of another triangle then the triangles are congruent.
Answer:
True

2. If two legs of a right-angled triangle are equal to two legs of another right-angled triangle then the right-angled triangles are congruent.
Answer:
True

3. If two triangles are congruent then the corresponding sides are equal.
Answer:
True

4. In ∆PQR, if PQ = PR and ∠P = 130° then ∠R = 70°.
Answer:
False

Match the following columns

Column I	Column II
If two sides and the included angle are equal in two triangles.	(a) ASA rule
If all three corresponding sides of two triangles are equal.	(b) SAS rule
If two angles and included side of two triangle are equal.	(c) SSS rule
In two right-angled triangles, hypotenuse and one side of two triangles are equal.	(d) RHS rule

Answer:

Column I	Column II
If two sides and the included angle are equal in two triangles.	(b) SAS rule
If all three corresponding sides of two triangles are equal.	(c) SSS rule
If two angles and included side of two triangle are equal.	(a) ASA rule
In two right-angled triangles, hypotenuse and one side of two triangles are equal.	(d) RHS rule

Very Short Answer Type Questions

Question 1.
In the given figure, if ∆ABC ≅ ∆PQR then find the value of x.

Answer:
4

Question 2.
In the following figure, show that ∆ABO = ∆ACO.

Answer:
Do Yourself

Question 3.
In a ∆ABC, AB = 5 cm, AC – 5 cm and ∠A = 50° then find ∠B.
Answer:
65°

Question 4.
In the given figure, if AB = AC, ∠ACB = 55° and ∠PAB = x then find the value of x.

Answer:
110°

Short Answer Type Questions

Question 1.
Give any two real-life examples for congruent shapes.
Answer:
Candy of the same type and same brand.
Soap of the same type and same brand.

Question 2.
In ∆ABC and ∆PQR, it is given that ∠A = ∠R, ∠C = ∠P and ∠B = ∠Q check both triangles are congruent or not.
Answer:
No

Question 3.
In an isosceles triangle, prove that the altitude from the vertex bisects the base.
Answer:
Do Yourself

Question 4.
If ∆DEF = ∆PQR, write the part(s) of ∆PQR that correspond to
(a) ∠F
(b) ∠E
(c) EF
Answer:
(a) ∠R
(b) ∠Q
(c) QR

Question 5.
∆DEF and ∆LMN are both isosceles with DE = DF and LM = LN, respectively.
If DE = LM and EF = MN then are the two triangles congruent? Which congruence criterion do you use? If ∠E = 40°, what is the measure of ∠N?
Answer:
Yes by SSS Criteria 40°

Question 6.
In the given figure, state the three pairs of equal parts in ∆ABC and ∆EOD. Is ∆ABC ≅ ∆EOD? Why?

Answer:
Yes by SSS Criteria

Question 7.
If ∆ABC ≅ ∆RPQ, ∠A = 60°, ∠B = 50° then find ∠P, ∠Q and ∠R.
Answer:
∠p = 50°
∠Q = 70°
∠R = 60°

Question 8.
∆ABC ≅ ∆DEF such that AB = DE, AC = DF and BC = EF. Find x and y on the basis of the data provided in the given figures.

Answer:
x = 45°
y = 30°

Long Answer Type Questions

Question 1.
In the following figure, ∆ABC and ∆DCB are right angled at A and D, respectively and AC = DB. Prove that ∆ABC = ∆DCB.

Answer:
Do yourself

Question 2.
In the following figure, PA ⊥ AB, QB ⊥ AB and PA = QB. Prove that ∆OAP ≅ ∆OBQ.

Answer:
Do yourself

Question 3.
In the given figure, state the three pairs of equal parts in ?ABC and ?DCB.

(a) Is ∆ABC ≅ ∆DCB? Why?
(b) Is AB = DC? Why?
(c) Is AC = DB? Why?
Answer:
(a) Yes, by ASA criteria
(b) Yes, by CPCT
(c) Yes, by CPCT

Question 10.
Rohan is an aspiring architect. He is observing a railway bridge made of steel beams. He notices that the structure is composed of several triangular sections. He focuses on one particular section, where two triangles, ∆ABC and ∆PQR are used to support a heavy load.
His supervisor informs him that these two triangles are exactly the same in shape and size, meaning that ∆ABC = ∆PQR under the correspondence A P, B Q and C R.
(i) If the length of side AB = 5 cm and BC = 7 cm, what must be the length of side PQ?
(ii) Rohan measures ∠ABC to be 60° and ∠BAC to be 80°. What is the measure of ∠PRQ.
(iii) Which congruence criterion would Rohan use if he only knew that AB = PQ, AC = PR and ∠BAC = ∠QPR?
Answer:
(i) 5 cm
(ii) 40°
(iii) SAS

Activity

Question 1.
Mirror Triangles
Rohan has a rectangular garden ABCD with a diagonal AC.

Answer the following questions.
(i) Identify the pair of congment triangles in rectangle ABCD.
(ii) Write the congruence statement correctly.
(iii) Which congruence rule is used?

Question 2.
Right Triangle Test
Shivam draw a right angled triangle with hypotenuse and one side of triangle are 5 cm and 4 cm, respectively and asked his friend to construct the same using the same data.
Answer the following questions from the given information.
(i) Are both triangles congruent?
(ii) Which parts are equal in both triangles?
(iii) Name the congruence rule used.

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