CBSE Class 7 Mathematics Geometric Twins Worksheet Set 01

Very Short Answer Questions

Question 1. What are congruent figures? Write the meaning in one line.
Answer:
Congruent figures are exact copies of each other: they have the same shape and the same size, so one fits exactly over the other.

Teacher's Note:
1. Both shape and size must match.
2. Superimposition is the test.

Question 2. Which symbol is used to show that two figures are congruent?
Answer:
The symbol ≅ is used. For example, △ ABC ≅ △ XYZ is read as “triangle ABC is congruent to triangle XYZ”.

Teacher's Note:
1. ≅ combines “same shape” (∼) and “equal” (=).
2. Write the vertices in matching order.

Question 3. Apart from sliding it, name the two things you are allowed to do to a figure before superimposing it on another figure while checking congruence.
Answer:
We may rotate (turn) it and we may flip (reflect) it, because neither changes its shape or size.

Teacher's Note:
1. Turning and flipping only change position.
2. Shape and size stay the same.

Question 4. Write the full form of the ASA condition for congruence.
Answer:
ASA stands for Angle Side Angle: two angles and the side lying between them.

Teacher's Note:
1. The middle letter is the included part.
2. Here the side lies between the two angles.

Question 5. Which single measurement is enough to draw a circle congruent to a given circle?
Answer:
The radius (or the diameter). Two circles with equal radii are congruent.

Teacher's Note:
1. All circles have the same shape.
2. Only the size has to be fixed.

Question 6. In a right-angled triangle, which side is called the hypotenuse?
Answer:
The side opposite the right angle is the hypotenuse; it is the longest side of the triangle.

Teacher's Note:
1. Look across from the right angle.
2. It is the H in RHS.

Question 7. State the SSS condition for the congruence of two triangles.
Answer:
If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

Teacher's Note:
1. No angle needs to be measured.
2. Three sides fix a triangle.

Question 8. What is the measure of each angle of an equilateral triangle?
Answer:
Each angle of an equilateral triangle is 60°.

Teacher's Note:
1. 180° ÷ 3 = 60°.
2. All three angles are equal.

Question 9. If △ ABC ≅ △ DEF, name the angle of △ ABC that is equal to ∠E.
Answer:
∠B, because B and E are both the second letters, so they correspond.

Teacher's Note:
1. Match the letters by position.
2. Second letter goes with second letter.

Question 10. Name the five conditions studied in this chapter that guarantee the congruence of two triangles.
Answer:
SSS, SAS, ASA, AAS and RHS.

Teacher's Note:
1. SSA and AAA are not on this list.
2. RHS is only for right-angled triangles.

Question 11. Are two triangles that have the same three angles always congruent? Answer in one line.
Answer:
No. Equal angles fix only the shape; the triangles can be of different sizes.

Teacher's Note:
1. AAA is not a congruence condition.
2. Think of a small and a large copy.

Question 12. In △ PQR, PQ = PR. Name the two angles of the triangle that are equal.
Answer:
∠Q = ∠R, because these angles lie opposite the equal sides PR and PQ.

Teacher's Note:
1. Angles opposite equal sides are equal.
2. The equal angles are at the ends of the third side.

Question 13. A bent-arm symbol on a signboard has arms AB = 4 cm and BC = 8 cm. Why are these two lengths alone not enough to redraw the symbol exactly, and what one more measurement is needed?
Answer:
The arms can be opened out by different amounts at B, so many different symbols have these two lengths. The angle between the arms, ∠ABC, must also be measured.

Teacher's Note:
1. Two lengths do not fix the opening.
2. The angle at B fixes it.

Question 14. Given that △ HEN ≅ △ BIG, write the side corresponding to EN and the angle corresponding to ∠N.
Answer:
H ↔ B, E ↔ I, N ↔ G. So EN corresponds to IG, and ∠N corresponds to ∠G.

Teacher's Note:
1. Write the matching pairs first.
2. Then read off the side and the angle.

Question 15. In △ ABC, AB = AC and ∠A = 50°. Find ∠B.
Answer:
AB = AC, so ∠B = ∠C. Then ∠B = (180° − 50°) ÷ 2 = 130° ÷ 2 = 65°.

Teacher's Note:
1. Base angles of an isosceles triangle are equal.
2. Share the remaining 130° equally.

Question 16. △ ABC ≅ △ XYZ. If ∠A = 55° and ∠Y = 65°, find ∠Z.
Answer:
∠X = ∠A = 55°. So ∠Z = 180° − 55° − 65° = 60°.

Teacher's Note:
1. Move the known angle to the same triangle first.
2. Then use the angle sum.

Question 17. In △ ABC and △ PQR, AB = PQ = 5 cm, BC = QR = 7 cm and ∠A = ∠P = 40°. Can you be sure that the triangles are congruent? Give a reason.
Answer:
No. The angle between AB and BC is ∠B, not ∠A. So this is the SSA case, which does not guarantee congruence.

Teacher's Note:
1. Find which angle lies between the two given sides.
2. A non-included angle gives SSA.

Question 18. In a rectangle ABCD, the diagonal BD is drawn. Which condition shows that △ ABD ≅ △ CDB?
Answer:
The SSS condition: AB = CD, AD = CB (opposite sides) and BD is common to both triangles.

Teacher's Note:
1. Opposite sides of a rectangle are equal.
2. The diagonal is a shared side.

Question 19. In △ ABC and △ PQR, ∠B = ∠Q = 90°, AC = PR and BC = QR. Write the congruence statement and name the condition used.
Answer:
△ ABC ≅ △ PQR by the RHS condition: right angles at B and Q, equal hypotenuses AC and PR, and equal sides BC and QR.

Teacher's Note:
1. AC and PR face the right angles, so they are hypotenuses.
2. Keep B with Q in the statement.

Question 20. If △ ABC ≅ △ XYZ, is it correct to write △ ACB ≅ △ XYZ? Give a reason.
Answer:
No. C corresponds to Z, not to Y. The correct rewriting is △ ACB ≅ △ XZY.

Teacher's Note:
1. Both names must be reordered together.
2. Check each letter pair.

Question 21. Name the condition that is satisfied when two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle.
Answer:
The SAS (Side Angle Side) condition, which guarantees congruence.

Teacher's Note:
1. The angle must be the included one.
2. The A sits between the two S's.

Question 22. In two triangles, two angles and a side that is not between those angles are equal. Explain in one line why the triangles are still congruent.
Answer:
The third angles are then also equal (angle sum 180°), so the data becomes ASA; this is the AAS condition, and the triangles are congruent.

Teacher's Note:
1. Two angles fix the third angle.
2. AAS can always be turned into ASA.

Question 23. Name one real-life structure in which congruent triangles can be seen, and say where they appear in it.
Answer:
Rabindra Setu (Howrah Bridge) in Kolkata: its steel framework is made of repeated congruent triangles. (The glass pyramid of the Louvre Museum is another example.)

Teacher's Note:
1. Repeated triangles make structures strong.
2. Other correct examples are also fine.

Question 24. Two rectangles each have a length of 8 cm. Can we say that they are congruent? Give a reason.
Answer:
No. Their breadths may be different. Rectangles are congruent only when both length and breadth are equal.

Teacher's Note:
1. One measurement does not fix a rectangle.
2. Both length and breadth are needed.

Question 25. In △ ABC, AB = AC and ∠B = 65°. Find ∠A.
Answer:
AB = AC, so ∠C = ∠B = 65°. Then ∠A = 180° − 65° − 65° = 50°.

Teacher's Note:
1. Both base angles are 65°.
2. Subtract both from 180°.

Question 26. In △ ABC and △ DEF, ∠A = ∠D = 90°, BC = EF and AB = DE. Name the condition that proves the congruence, and name the hypotenuse of each triangle.
Answer:
The RHS condition proves △ ABC ≅ △ DEF. The hypotenuse of △ ABC is BC and that of △ DEF is EF, as each lies opposite the right angle.

Teacher's Note:
1. The right angle here is at A and D.
2. So the hypotenuse is the side not touching A or D.

Question 27. In a figure, AB = AD, CB = CD and AC is joined. Give the reason, in one line, why AC divides ∠BAD into two equal parts.
Answer:
△ ABC ≅ △ ADC by SSS (AB = AD, CB = CD, AC common), so the corresponding angles ∠BAC and ∠DAC are equal.

Teacher's Note:
1. First prove the triangles congruent.
2. Then use corresponding angles.

Question 28. While constructing a triangle from two sides and an angle that is not between them, the arc cuts the drawn ray at two different points. What does this tell us about the SSA condition?
Answer:
Two different triangles fit the same measurements, so the SSA condition does not guarantee congruence.

Teacher's Note:
1. Two answers means the data does not fix the triangle.
2. This is why SSA is not a rule.

Question 29. ABCD is a square and the diagonal AC is drawn. Write two different correct congruence statements that connect △ ABC with the other triangle formed.
Answer:
△ ABC ≅ △ ADC (SSS: AB = AD, BC = DC, AC common) and also △ ABC ≅ △ CDA.

Teacher's Note:
1. All four sides of a square are equal.
2. So the triangle can be matched in two ways.

Question 30. The segments AD and BC meet at a point O such that OA = OD and OB = OC. Explain in one line why AB is parallel to CD.
Answer:
△ AOB ≅ △ DOC by SAS (OA = OD, OB = OC, vertically opposite angles at O), so ∠OAB = ∠ODC; these are equal alternate angles for the transversal AD, so AB ∥ CD.

Teacher's Note:
1. Equal alternate angles mean parallel lines.
2. Congruence gives the equal angles.