Class 7 Maths Chapter 1 Geometric Twins worksheet with MCQs, short answer questions, practice questions and extra questions based on Ganita Prakash Part 2 for revision and exam preparation.
Class 7 Mathematics
Ganita Prakash – Part II
Chapter 1 – Geometric Twins
Fresh Practice Worksheet
Part A – Extra Practice Questions
Attempt these questions first. Write your answers in the spaces provided.
1. Fill in the blanks.
- Figures having exactly the same shape and size are called __________ figures.
- The three conditions of SSS involve three corresponding __________.
- The side opposite the right angle in a triangle is called the __________.
- In SAS, the angle must be the __________ angle between the two given sides.
- Each angle of an equilateral triangle measures __________.
2. State whether the following statements are True or False.
- Congruent figures must have the same colour.
- Congruent figures can be rotated before being superimposed.
- Two triangles with three corresponding equal sides are congruent.
- SSA always proves that two triangles are congruent.
- All three angles of an equilateral triangle are equal.
- Two congruent figures can have different sizes.
3. Name the congruence condition.
- Three corresponding sides are equal.
- Two sides and the included angle are equal.
- Two angles and the included side are equal.
- Two angles and a non-included side are equal.
- A right angle, hypotenuse and one corresponding side are equal.
- Two sides and a non-included angle are given.
4. Two triangles have sides 5 cm, 6 cm and 7 cm each. Are the triangles necessarily congruent? Give a reason.
5. Two triangles have angles 40°, 60° and 80°. Are they necessarily congruent? Explain.
6. If two sides of a triangle are equal, what can you say about the angles opposite those sides?
7. Find all three angles of an equilateral triangle.
8. If ΔABC ≅ ΔPQR, write the corresponding vertices, sides and angles.
| Type | Corresponding Parts |
|---|---|
| Vertices | |
| Sides | |
| Angles |
9. In ΔABC, AB = AC and ∠A = 50°. Find ∠B and ∠C.
10. A right triangle has hypotenuse 10 cm and one side 6 cm. Another right triangle has the same hypotenuse and corresponding side. Are the triangles congruent? State the condition.
11. Explain why SSA is not always sufficient to prove two triangles congruent.
12. Complete the table.
| Given Information | Congruence Condition |
|---|---|
| Three corresponding sides are equal | |
| Two sides and included angle are equal | |
| Two angles and included side are equal | |
| Two angles and non-included side are equal | |
| Right angle, hypotenuse and one side are equal |
13. Can a figure be congruent to its mirror image? Explain.
14. If ΔABC ≅ ΔDEF, complete the following.
- AB = __________
- BC = __________
- AC = __________
- ∠A = __________
- ∠B = __________
- ∠C = __________
15. A square ABCD is divided by diagonal AC. Which two triangles are congruent? Give a reason.
Draw the square and diagonal AC here.
16. Draw two congruent triangles. Mark at least three pairs of corresponding parts.
Draw your triangles here.
17. A triangle has sides 7 cm, 8 cm and 9 cm. Another triangle has sides 9 cm, 7 cm and 8 cm. Are they congruent? Give a reason.
18. Explain why AAA is not a congruence condition.
19. If AB = AC in an isosceles triangle and ∠A = 80°, find ∠B and ∠C.
20. Draw an example of two triangles that are congruent by SSS.
Draw your triangles here.
Part B – Book Questions
Solve the following textbook questions in order.
1. Check if the two figures are congruent.
Observe the figures in the textbook and compare them here.
2. Circle the pairs that appear congruent.
Use the figures given in the textbook.
3. What measurements would you take to create a figure congruent to a given:
(a) Circle
(b) Rectangle
Using this, state how would you check if two—
(a) Circles are congruent?
(b) Rectangles are congruent?
4. How would we check if two figures like the one below are congruent?
Use the figure given in the textbook.
Use this to identify whether each of the following pairs are congruent.
Figure it Out – 1. Suppose ΔHEN is congruent to ΔBIG. List all the other correct ways of expressing this congruence.
Figure it Out – 2. Determine whether the triangles are congruent. If yes, express the congruence.
Use the triangle measurements shown in the textbook.
Figure it Out – 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.
Draw or use the textbook figure.
Figure it Out – 4. In the figure below, are ΔDFE and ΔGED congruent to each other? It is given that DF = DG and FE = GE.
Draw or use the textbook figure.
Figure it Out – 1. Identify whether the triangles below are congruent. What conditions did you use to establish their congruence? Express the congruence.
Use the textbook figure with the given measurements.
Figure it Out – 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.)
Draw or use the textbook figure.
Figure it Out – 3. Given that ∠ABC = ∠DBC and ∠ACB = ∠DCB, show that ∠BAC = ∠BDC. Are the two triangles congruent?
Figure it Out – 4. Identify the equal parts in the following figure, given that ∠ABD = ∠DCA and ∠ACB = ∠DBC.
Use the textbook figure.
Measuring Two Angles and a Non-Included Side
The following triangles ΔABC and ΔXYZ are such that ∠A = ∠X = 35°, ∠C = ∠Z = 75°, and BC = YZ = 4 cm. Are the triangles congruent? Give a reason.
Figure it Out – 1. Identify the pairs in which the triangles are congruent, 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
Figure it Out – 2. Given that OB = OC, and OA = OD. Show that AB is parallel to CD.
Draw or use the textbook figure.
Figure it Out – 3. ABCD is a square. Show that ΔABC ≅ ΔADC. Is ΔABC also congruent to ΔCDA?
Draw square ABCD and diagonal AC.
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?
5. Find ∠B and ∠C, if A is the centre of the circle.
Use the 120° diagram from the textbook.
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.
Use the complete angle diagram from the textbook.
Answer Sheet
Use this section after completing the worksheet. The answers are intentionally kept separate from the questions.
Part A – Extra Practice Answers
| Question | Answer |
|---|---|
| 1 | 1. congruent 2. sides 3. hypotenuse 4. included 5. 60° |
| 2 | False, True, True, False, True, False |
| 3 | 1. SSS 2. SAS 3. ASA 4. AAS 5. RHS 6. SSA |
| 4 | Yes, by SSS. |
| 5 | No. Equal angles alone do not determine the size of a triangle. |
| 6 | The angles opposite equal sides are equal. |
| 7 | 60°, 60°, 60° |
| 8 | A ↔ P, B ↔ Q, C ↔ R; AB ↔ PQ, BC ↔ QR, AC ↔ PR; ∠A ↔ ∠P, ∠B ↔ ∠Q, ∠C ↔ ∠R. |
| 9 | ∠B = 65°, ∠C = 65° |
| 10 | Yes, by RHS. |
| 11 | SSA does not always guarantee congruence because it can produce two different triangles. |
| 12 | SSS, SAS, ASA, AAS, RHS |
| 13 | Yes. A figure may be flipped or reflected and still be congruent if it has exactly the same shape and size. |
| 14 | AB = DE; BC = EF; AC = DF; ∠A = ∠D; ∠B = ∠E; ∠C = ∠F. |
| 15 | ΔABC ≅ ΔADC by SSS. |
| 16 | Answers may vary. The two triangles must have exactly the same shape and size. |
| 17 | Yes, by SSS. |
| 18 | AAA determines shape but not size, so it does not guarantee congruence. |
| 19 | ∠B = 50°, ∠C = 50° |
| 20 | Answers may vary. Three corresponding equal sides must be shown. |
Part B – Book Questions
| Question | Answer / Key Idea |
|---|---|
| 1 | Check whether the figures can be exactly superimposed after rotation or flipping. |
| 2 | Select the pairs having exactly the same shape and size. |
| 3(a) | Measure the radius or diameter of the circle. |
| 3(b) | Measure the length and breadth of the rectangle. |
| Using this | Circles: equal radii. Rectangles: equal corresponding lengths and breadths. |
| 4 | Compare corresponding sides and angles and check whether one figure can be superimposed on the other. |
| Figure it Out – 1 | Maintain the correspondence H ↔ B, E ↔ I, N ↔ G while writing other valid congruence orders. |
| Figure it Out – 2 | Use the three corresponding equal side lengths; congruence is by SSS. |
| Figure it Out – 3 | ΔABC ≅ ΔADC by SSS. Therefore AC bisects the relevant angles. |
| Figure it Out – 4 | ΔDFE ≅ ΔDGE by SSS. |
| Figure it Out – SAS | Use the two equal sides and included equal angle; congruence is by SAS. |
| Parallel Lines Question | Use alternate interior angles, AB = CD and the corresponding common side to establish congruence. |
| Angle Question | ∠BAC = ∠BDC. The two equal angles alone do not necessarily prove congruence. |
| Equal Parts Question | Identify the corresponding angles and sides from the given angle equalities and the figure. |
| Measuring Two Angles and a Non-Included Side | Yes. The triangles are congruent by ASA. |
| Congruence Pairs | (a) SSS; (b) SAS; (c) RHS; (d) AAS; (e) determine from the included-angle position in the given figure. |
| OB = OC, OA = OD | Use SAS with the vertically opposite angles to prove the triangles congruent and then use alternate interior angles to show AB ∥ CD. |
| Square ABCD | ΔABC ≅ ΔADC by SSS. The same triangles can also be written in another valid corresponding order. |
| Two Different Ways | Use symmetric or congruent triangles and maintain correct vertex correspondence. |
| Six Different Ways | An equilateral triangle provides six possible vertex correspondences with another equilateral triangle. |
| 5 | ∠B = 30°, ∠C = 30°. |
| 6 | Use equal sides, equal opposite angles, vertically opposite angles, and the angle-sum property of triangles. |
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