NCERT Class 7 Maths Part 2 Chapter 1 Geometric Twins Worksheet with Answers

Class 7 Maths Part 2 Chapter 1 Worksheet

Fill in the Blanks

1. Figures having the same shape and the same size are called __________ figures.
Answer: Congruent

2. A square has __________ lines of symmetry.
Answer: 4

3. A rectangle has __________ lines of symmetry.
Answer: 2

4. Reflection produces a __________ image.
Answer: Mirror

5. Translation means __________ a figure without turning it.
Answer: Sliding

Write True or False

6. All congruent figures are similar.
Answer: True

7. A circle has infinitely many lines of symmetry.
Answer: True

8. A scalene triangle has no line of symmetry.
Answer: True

9. Rotation changes the size of a figure.
Answer: False

10. Symmetry is commonly found in nature and architecture.
Answer: True

Short Answer Questions

11. What are congruent figures?
Answer: Congruent figures have the same shape and the same size.

12. How many lines of symmetry does an equilateral triangle have?
Answer: 3

13. Name any one transformation that changes only the position of a figure.
Answer: Translation (or Rotation/Reflection)

14. Give one real-life example of symmetry.
Answer: Butterfly, leaf, or human face.

15. Why is symmetry important in geometry?
Answer: It helps us understand balanced shapes, patterns, designs, and geometric constructions.

NCERT Class 7 Maths Part 2 Chapter 1 Geometric Twins MCQ Questions with Answers

Class 7 Maths Part 2 Chapter 1 MCQs

1. Congruent figures have:
A. Different shapes and sizes
B. Same shape and same size
C. Same shape but different sizes
D. Different shapes but same size
Answer: B

2. Similar figures have:
A. Same shape only
B. Same size only
C. Different shape and size
D. Same shape and same size only
Answer: A

3. Which shape has four lines of symmetry?
A. Rectangle
B. Square
C. Triangle
D. Pentagon
Answer: B

4. A rectangle has how many lines of symmetry?
A. 1
B. 2
C. 3
D. 4
Answer: B

5. An equilateral triangle has:
A. 1 line of symmetry
B. 2 lines of symmetry
C. 3 lines of symmetry
D. 4 lines of symmetry
Answer: C

6. A circle has:
A. No line of symmetry
B. One line of symmetry
C. Two lines of symmetry
D. Infinitely many lines of symmetry
Answer: D

7. Reflection produces a:
A. Mirror image
B. Bigger figure
C. Smaller figure
D. Curved figure
Answer: A

8. Rotation means:
A. Sliding a figure
B. Turning a figure around a fixed point
C. Stretching a figure
D. Folding a figure
Answer: B

9. Translation means:
A. Flipping a figure
B. Sliding a figure without turning it
C. Enlarging a figure
D. Cutting a figure
Answer: B

10. All congruent figures are:
A. Similar
B. Different
C. Unequal
D. None of these
Answer: A

11. Which of the following is an example of symmetry in nature?
A. Butterfly
B. Rock
C. Cloud
D. River
Answer: A

12. Which transformation changes only the position of a figure?
A. Reflection
B. Rotation
C. Translation
D. All of the above
Answer: D

13. A line of symmetry divides a figure into:
A. Two equal halves
B. Three equal parts
C. Four equal parts
D. Unequal parts
Answer: A

14. Which shape has no line of symmetry?
A. Scalene triangle
B. Square
C. Circle
D. Rectangle
Answer: A

15. Symmetry is widely used in:
A. Art and architecture
B. Nature and design
C. Engineering and logos
D. All of the above
Answer: D

NCERT Class 7 Maths Part 2 Chapter 1 Geometric Twins Extra Questions with Answers

Class 7 Maths Part 2 Chapter 1 Extra Questions with Answers

Q1. What are congruent figures?
Answer: Congruent figures have the same shape and the same size.

Q2. Can two congruent figures have different orientations?
Answer: Yes.

Q3. What is meant by symmetry?
Answer: Symmetry means a figure can be divided into two identical halves.

Q4. How many lines of symmetry does a square have?
Answer: 4

Q5. How many lines of symmetry does a rectangle have?
Answer: 2

Q6. How many lines of symmetry does an equilateral triangle have?
Answer: 3

Q7. How many lines of symmetry does a circle have?
Answer: Infinitely many.

Q8. Are all similar figures congruent?
Answer: No.

Q9. Are all congruent figures similar?
Answer: Yes.

Q10. Which transformation keeps the size and shape of a figure unchanged?
Answer: Reflection, rotation, and translation.

Q11. What is the mirror line of a figure called?
Answer: Line of symmetry.

Q12. Name one real-life object having symmetry.
Answer: Butterfly.

Q13. What do we call figures with the same shape but different sizes?
Answer: Similar figures.

Q14. Why is symmetry important in geometry?
Answer: It helps us understand patterns, designs, and balanced shapes.

Q15. Where is symmetry used in daily life?
Answer: In architecture, rangoli, logos, art, nature, engineering, and design.

Figure it Out (Page 3 – 4)

1. Check if the two figures are congruent.

Solution:

Although both figures have the same arm lengths, their included angles are different. Therefore, the two figures are not congruent

2. Circle the pairs that appear congruent.

Solution:

3. What measurements would you take to create a figure congruent to a given:
(a) Circle
(b) Rectangle
Solution:
(a) To create a circle congruent to a given circle, measure only the radius.
(b) To create a rectangle congruent to a given rectangle, measure both the length and the breadth.

Q. Using this, state how would you check if two —
(a) Circles are congruent?
(b) Rectangles are congruent?
Solution:
(a) Two circles are congruent if they have the same radius.
(b) Two rectangles are congruent if they have the same length and the same breadth.

4. How would we check if two figures like the one below are congruent?

Solution:
If two figures have the same arm lengths and the angle between those arms is equal, then the figures are congruent.

Q. Use this to identify whether each of the following pairs are congruent.

Solution:
Both pairs are congruent because their arm lengths and the included angles between them are equal.

Figure it Out (Page 8 – 9)

1. Suppose ∆HEN is congruent to ∆BIG. List all the other correct ways of expressing this congruence.
Solution:
If ∆HEN ≅ ∆BIG, then the correspondence is:
H ↔ B
E ↔ I
N ↔ G
All the six correct ways of expressing the congruence are:
1. ∆HEN ≅ ∆BIG
2. ∆ENH ≅ ∆IGB
3. ∆NHE ≅ ∆GBI
4. ∆EHN ≅ ∆IBG
5. ∆HNE ≅ ∆BGI
6. ∆NEH ≅ ∆GIB

2. Determine whether the triangles are congruent. If yes, express the congruence.

Solution:
In △RED and △JAM,
RE = JA = 3.5 cm
ED = AM = 5 cm
RD = JM = 6 cm
Thus, the triangles satisfy the SSS condition.
So, the congruence is written as:
ΔRED ≅ ΔJAM.

3. In the figure below, AB = AD, CB = CD.
Can you identify any pair of congruent triangles? If yes, explain why they are congruent.
Does AC divide ∠BAD and ∠BCD into two equal parts? Give reasons.

Solution:
In △ABC and △ADC,
AB = AD …….. (Given)
CB = CD …….. (Given)
AC = AC …….. (Common side)
Thus, the traingles satisfy the SSS condition.
Hence, △ABC ≅ △ ADC.
Thererfore, the corresponding equal parts are:
∠BAC = ∠DAC. Hence, AC bisects ∠BAD.
∠BCA = ∠DCA. Hence, AC bisects ∠BCD.

4. In the figure below, are ΔDFE and ΔGED congruent to each other? It is given that DF = DG and FE = GE.

Solution:
In ΔDFE and ΔDGE,
DF = DG …….. (Given)
FE = GE …….. (Given)
DE = DE …….. (Common)
Thus, the triangles satisfy the SSS codition.
Hence, ΔDFE ≅ ΔDGE.

Figure it Out (Page 13 – 14)

1. Identify whether the triangles below are congruent. What conditions did you use to establish their congruence? Express the congruence.

Solution:
In △ABC and △XZY,
AB = XZ = 7 cm ……. (given)
BC = ZY = 5 cm …….. (given)
∠B = ∠Z = 47° ……… (given)
Thus, the triangles satisfy the SAS condition..
So, the congruence is written as:
△ABC ≅ △XZY.

2. Given that CD and AB are parallel, and AB = CD, what are the other equal parts in this figure? (Hint: When the lines are parallel, the alternate angles are equal. Are the two resulting triangles congruent? If so, express the congruence.)

Solution:
Since AB ∥ CD, the transversal lines AC and BD form alternate interior angles.
So,
∠OAB = ∠OCD ……….. (alternate interior angles)
∠OBA = ∠ODC ………… (alternate interior angles)
Also, it is given that AB = CD.
In triangles △OAB and △OCD,
AB = CD ……. (given)
∠OAB = ∠OCD ……….. (alternate interior angles)
∠OBA = ∠ODC ………… (alternate interior angles)
Thus, the triangles satisfy the ASA condition.
Hence, △OAB ≅ △OCD.

Therefore, the corresponding equal parts are OA = OC, OB = OD, ∠AOB = ∠COD.

3. Given that ∠ABC = ∠DBC and ∠ACB = ∠DCB, show that ∠BAC = ∠BDC. Are the two triangles congruent?

Solution:
In triangles △ABC and △DBC,
∠ABC = ∠DBC ………. (given)
BC = BC ………… (common side)
∠ACB = ∠DCB ………. (given)
Thus, the triangles satisfy the ASA condition.
Hence, △ABC ≅ △DBC.
Therefore, the corresponding equal parts are ∠BAC = ∠BDC.

4. Identify the equal parts in the following figure, given that ∠ABD = ∠DCA and ∠ACB = ∠DBC.

Solution:
∠ABD = ∠DCA and ∠ACB = ∠DBC …………. (given)
∠ABD + ∠DBC = ∠ABC
∠DCA + ∠ACB = ∠DCB

In △ABC and △DCB,
∠ABC = ∠DCB ……… (proved above)
BC = CB ………… (common side)
∠ACB = ∠DBC ………… (given)
Thus, the triangles satify the ASA condition.
Hence, △ABC ≅ △DCB.
Therefore, the corresponding equal parts are:
AB = DC, AC = DB, ∠BAC = ∠CDB.

Figure it Out (Page 13 – 14)

1. ∆AIR ≅ ∆FLY. Identify the corresponding vertices, sides and angles.
Solution:
In ∆AIR ≅ ∆FLY,
The corresponding vertices are A ↔ F, I ↔ L, R ↔ Y.
The corresponding sides are AI = FL, IR = LY, AR = FY.
The corresponding angles are ∠A = ∠F, ∠I = ∠L, ∠R = ∠Y.

2. Each of the following cases contains certain measurements taken from two triangles. Identify the pairs in which the triangles are congruent to each other, with reason. Express the congruence whenever they are congruent.
(a) AB = DE
BC = EF
CA = DF
(b) AB = EF
∠A =∠E
AC = ED
(c) AB = DF
∠B = ∠D = 90°
AC = FE
(d) ∠A = ∠D
∠B = ∠E
AC = DF
(e) AB = DF
∠B = ∠F
AC = DE
Solution:
(i) AB = DE, BC = EF, CA = DF
All three corresponding sides are equal.
Thus, the triangles satisfy the SSS condition.
Hence, △ABC ≅ △DEF.

(ii) AB = EF, ∠A =∠E, AC = ED
Two corresponding sides and the included angle are equal.
Thus, the triangles satisfy the SAS condition.
Hence, △ABC ≅ △EFD.

(iii) AB = DF, ∠B = ∠D = 90°, AC = FE
The triangles have equal right angles, equal hypotenuses, and one equal corresponding side.
Thus, the triangles satisfy the RHS condition.
Hence, △ABC ≅ △FDE.

(iv) ∠A = ∠D, ∠B = ∠E, AC = DF
Two corresponding angles and one corresponding side are equal.
Thus, the triangles satisfy the AAS condition.
Hence, △ABC ≅ △DEF.

(v) AB = DF, ∠B = ∠F, AC = DE
Here, two corresponding sides and a non-included angle are equal.
Thus, the triangles satisfy the SSA condition, which is not a valid congruence rule.
Hence, △ABC need not be congruent to △DFE.

3. It is given that OB = OC, and OA = OD. Show that AB is parallel to CD.
[Hint: AD is a transversal for these two lines. Are there any equal alternate angles?]

Solution:
In △AOB and △DOC,
OA = OD ……… (given)
OB = OC ………… (given)
∠AOB = ∠DOC ………… (vertically opposite angles)
Thus, the triangles satify the SAS condition.
Hence, △AOB ≅ △DOC.

Therefore, the corresponding equal parts are: ∠OAB = ∠ODC and ∠OBA = ∠OCD.
Since these angles are alternate interior angles formed by the transversal AD and BC with the pair of lines AB and CD.
Hence, AB Ⅱ CD.

4. ABCD is a square. Show that ∆ABC ≅ ∆ADC. Is ∆ABC also congruent to ∆CDA?

Give more examples of two triangles where one triangle is congruent to the other in two different ways, as in the case above. Can you give an example of two triangles where one is congruent to the other in six different ways?
Solution:
In square ABCD, all sides are equal.
So,
In △ABC and △ADC,
AB = CD
BC = AD
Diagonal AC is common.
Thus, the triangles follow the SSS condition.
Hence, △ABC ≅ △ ADC
Yes, △ABC is also congruent to △CDA, because △CDA is the same triangle as △ADC written in a different order.

5. Find ∠B and ∠C, if A is the centre of the circle.

Solution:
In △ABC,
AB = AC (radius of circle)
∠C = ∠B (angles opposite to equal sides are equal)
Also,
∠C + ∠B + ∠BAC = 180° (sum of angles of triangle)
∠B + ∠B + 120° = 180°
2∠B = 180° – 120°
2∠B = 60°
∠B = 60°/2 = 30°
Therefore, ∠C = ∠B = 30°.

6. Find the missing angles. As per the convention that we have been following, all line segments marked with a single ‘|’ are equal to each other and those marked with a double ‘|’ are equal to each other, etc.

Solution:
Do it yourself.