Question 1

Check if the two figures are congruent.

Accepted Answer

Let’s measure the angles above with a protractor.
We found as follows:
Here, ∠ABC does not coincide with ∠DEF.
Hence, the given figures are not congruent.

Source: This question is from Geometric Twins, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Geometric Twins: Check, Figures, Congruent, Geometric Twins, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Geometric TwinsQ2: Circle the pairs that appear congruent.
Q3: What measurements would you take to create a figure congruent to a given: (a) Circle (b) Rectangle...
Q4: How would we check if two figures like the one below are congruent? Use this to identify whether...
Q5: Find ∠B and ∠C, if A is the centre of the circle.
Q6: Find the missing angles. As per the convention that we have been following, all line segments...
Practice more questions from Geometric Twins &mdash; Mathematics, Class 7 CBSE

Question 2

Circle the pairs that appear congruent.

Accepted Answer

(a) and (d) are congruent. As they can be superimposed exactly.

Source: This question is from Geometric Twins, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Geometric Twins: Circle, Pairs, Appear, Congruent, Geometric Twins, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Geometric TwinsQ3: What measurements would you take to create a figure congruent to a given: (a) Circle (b) Rectangle...
Q4: How would we check if two figures like the one below are congruent? Use this to identify whether...
Q5: Find ∠B and ∠C, if A is the centre of the circle.
Q6: Find the missing angles. As per the convention that we have been following, all line segments...
Practice more questions from Geometric Twins &mdash; Mathematics, Class 7 CBSE

Question 3

What measurements would you take to create a figure congruent to a given:
(a) Circle
(b) Rectangle
Using this, state how you would check if two
(a) Are circles congruent?
(b) Rectangles are congruent?

Accepted Answer

(a) I will measure the radius or diameter of the given circle.
(b) I will measure the length and breadth of the given rectangle.
(a) I will place one circle over another circle.
If they exactly superimpose, they are congruent.
In this case, both will have the same radius.
(b) I will place one rectangle over another rectangle.
If they exactly superimpose, they are congruent.
In such a case, both will have the same length and breadth.

Question 4

How would we check if two figures like the one below are congruent?
Use this to identify whether each of the following pairs is congruent.

Accepted Answer

To check if the two figures are congruent, one would need to measure the lengths of the corresponding line segments and the angle between them.
Yes, each of the given figures is congruent. Length of line segments in each figure is 3.3 cm (Horizontal line) and 2.3 cm (Vertical line), and the angle between them is 82°.
1.2 Congruence of Triangles
Figure It Out (Pages 8-9)

Question 5

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

Accepted Answer

In ∆BAC
AB = AC = Radius of the circle.
Let ∠ABC = ∠ACB = x (angles opposite to equal sides are equal)
Then, x + x + 120° = 180° (∵ Sum of all the angles in a triangle is 180°)
⇒ 2x = 180° – 120°
⇒ 2x = 60°
⇒ x = 30°
Hence ∠B = ∠C = 30°

Question 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.

Accepted Answer

In ∆CUR
∠CUR = ∠CRU = x (say)
(∵ CU = CR)
According to the angle sum property of a triangle
x + x + 90° = 180°
⇒ 2x = 180° – 90° = 90°
⇒ x = 45°
∴ ∠CUR = ∠CRU = 45°
In ∆VRN
∠VRN = ∠VNR = a (say)
[∵ Angles opposite to equal sides are equal]
∵ VR = VN
Since the sum of the angles of a triangle is 180°.
So, a + a + 68° = 180°
⇒ 2a = 180° – 68°
⇒ 2a = 112°
⇒ a = 56°
∠VRN = ∠VNR = 56°
In ∆AUP
∠UAP = ∠UPA (∵ they are equal)
∠UPA = 56°
The sum of the angles of a triangle is 180°.
So, 56° + 56° + ∠AUP = 180°
⇒ 112° + ∠AUP = 180°
⇒ ∠AUP = 180° – 112°
⇒ ∠AUP = 68°
∆BOF is an equilateral triangle as all sides are equal.
So, OB = OF = BF
∠FOB = ∠FBO = ∠OFB = 60°
∠RVN + ∠DVN = 180°
⇒ 68° + ∠DVN = 180°
⇒ ∠DVN = 180° – 68°
⇒ ∠DVN = 112°
∠VND + ∠VDN + ∠NVD = 180°
∵ VN = VD
∴ ∠VND = ∠VDN = c
∴ c + c + 112° = 180°
⇒ 2c = 180° – 112°
⇒ 2c = 68°
⇒ c = 34°
∠VND = ∠VDN = 34°
In ∆OLB
∠OBL = 90° – 60° = 30°
∠LOB = 60° [∵ LO || BF and BO is transversal]
In ∆OPN
∠OPN + ∠PON + ∠PNO = 180°
⇒ ∠OPN + 56° + 90° = 180°
⇒ ∠OPN + 146° = 180°
⇒ ∠OPN = 180° – 146°
⇒ ∠OPN = 34°
Now, ∠APK + ∠KPO + ∠OPN = 180° [∵ Straight angle is 180°]
⇒ 44° + ∠KPO + 34° = 180°
⇒ ∠KPO = 180° – 78°
⇒ ∠KPO = 102°
In ∆KPO
∠KPO + ∠POK + ∠PKO = 180°
⇒ 102° + 30° + ∠PKO = 180°
⇒ 132° + ∠PKO = 180°
⇒ ∠PKO = 180° – 132° = 48°
∠KAP + ∠KPA + ∠AKP = 180° [∵ Sum of angles of a triangle is 180°]
⇒ 34° + 44° + ∠AKP = 180°
⇒ 78° + ∠AKP = 180°
⇒ ∠AKP = 180° – 78°
⇒ ∠AKP = 102° and ∠PKO = 48°
So, ∠AKP + ∠PKO + ∠OKL = 180°
⇒ 102° + 48° + ∠OKL = 180°
⇒ 150° + ∠OKL = 180°
⇒ ∠OKL = 180° – 150°
⇒ ∠OKL = 30°
In ∆KOL
∠OKL + ∠OLK + ∠KOL = 180°
⇒ 30° + 90° + ∠KOL = 180°
⇒ ∠KOL = 180° – 120°
⇒ ∠KOL = 60°
Also, ∆OKL ≅ ∆OBL
KL = LB
∠OLK ≅ ∠OLB = 90°
Side angle side condition.