Chapter-9 Geometric Twins — Online MCQ Test
MATHS · Grade 7 · CBSE(NCERT)
Practice Chapter-9 Geometric Twins with a free chapter-wise online MCQ test.
This chapter covers: congruence - SSS - SAS - ASA - RHS.
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter-9 Geometric Twins — Important Questions & Answers
What does the term 'congruent' mean in geometry?
- A. Figures that have the same shape but different sizes
- B. Figures that have exactly the same shape and size
- C. Figures that have different shapes but equal areas
- D. Figures that are similar but not identical
Answer: B. Figures that have exactly the same shape and size
Congruent figures have the same shape and size. When two figures are congruent, they can be superimposed on each other perfectly.
Congruent figures have the same shape and size. When two figures are congruent, they can be superimposed on each other perfectly.
Which symbol is used to denote congruence between two figures?
- A. =
- B. ≈
- C. ≅
- D. ~
Answer: C. ≅
The symbol ≅ is used to denote congruence between two geometric figures.
The symbol ≅ is used to denote congruence between two geometric figures.
SSS rule stands for _____ in congruence of triangles.
- A. Side-Side-Side
- B. Shape-Size-Side
- C. Single-Side-Set
- D. Similarity-Side-Sum
Answer: A. Side-Side-Side
SSS stands for Side-Side-Side, which is a criterion for triangle congruence when all three sides of one triangle are equal to the three sides of another triangle.
SSS stands for Side-Side-Side, which is a criterion for triangle congruence when all three sides of one triangle are equal to the three sides of another triangle.
What does SAS criterion for congruence mean?
- A. Side-Angle-Side
- B. Sum-Angle-Sum
- C. Similar-Adjacent-Side
- D. Side-Adjacent-Sum
Answer: A. Side-Angle-Side
SAS stands for Side-Angle-Side. Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding parts of another triangle.
SAS stands for Side-Angle-Side. Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding parts of another triangle.
Two triangles have all three sides equal. Which congruence criterion is satisfied?
- A. SAS
- B. ASA
- C. SSS
- D. RHS
Answer: C. SSS
When all three sides of one triangle are equal to the three sides of another triangle, the SSS (Side-Side-Side) criterion is satisfied.
When all three sides of one triangle are equal to the three sides of another triangle, the SSS (Side-Side-Side) criterion is satisfied.
Triangle ABC has AB = DE, angle B = angle E, and BC = EF. Which congruence rule applies?
- A. SSS
- B. SAS
- C. ASA
- D. RHS
Answer: B. SAS
We have two sides (AB = DE, BC = EF) and the included angle (angle B = angle E) between them equal. This satisfies the SAS criterion.
We have two sides (AB = DE, BC = EF) and the included angle (angle B = angle E) between them equal. This satisfies the SAS criterion.
If triangle ABC ≅ triangle XYZ, then which of the following is NOT necessarily true?
- A. AB = XY
- B. BC = YZ
- C. Angle A = Angle X
- D. Area of ABC = Area of XYZ and the perimeters are different
Answer: D. Area of ABC = Area of XYZ and the perimeters are different
If two triangles are congruent, their corresponding sides are equal, so their perimeters are also equal. The option stating different perimeters is incorrect.
If two triangles are congruent, their corresponding sides are equal, so their perimeters are also equal. The option stating different perimeters is incorrect.
Triangle PQR has PQ = 6 cm, QR = 8 cm, and PR = 10 cm. Triangle ABC has AB = 8 cm, BC = 10 cm, and AC = 6 cm. Are these triangles congruent?
- A. No, because the sides are in different order
- B. Yes, by SSS criterion
- C. No, because one side is different
- D. Cannot be determined
Answer: B. Yes, by SSS criterion
Both triangles have sides of length 6 cm, 8 cm, and 10 cm. By SSS criterion, the triangles are congruent regardless of the order in which the sides are listed.
Both triangles have sides of length 6 cm, 8 cm, and 10 cm. By SSS criterion, the triangles are congruent regardless of the order in which the sides are listed.
Which statement about congruence is ALWAYS true?
- A. Congruent triangles have equal areas but different perimeters
- B. Congruent figures have equal areas and equal perimeters
- C. Similar triangles are always congruent
- D. Congruent triangles have different corresponding angles
Answer: B. Congruent figures have equal areas and equal perimeters
If two figures are congruent, they have the same shape and size, which means they have equal areas and equal perimeters.
If two figures are congruent, they have the same shape and size, which means they have equal areas and equal perimeters.
In right triangle ABC with right angle at B, AB = 6 cm and AC = 10 cm. In right triangle PQR with right angle at Q, PR = 10 cm and PQ = 6 cm. Which criterion proves congruence, and what is BC?
- A. RHS; BC = 8 cm
- B. SSS; BC = 9 cm
- C. SAS; BC cannot be determined
- D. ASA; BC = 6 cm
Answer: A. RHS; BC = 8 cm
Using Pythagoras theorem, BC = √(AC² - AB²) = √(100 - 36) = 8 cm. Both triangles have the right angle, hypotenuse (AC = PR = 10 cm), and one leg (AB = PQ = 6 cm) equal, satisfying RHS criterion.
Using Pythagoras theorem, BC = √(AC² - AB²) = √(100 - 36) = 8 cm. Both triangles have the right angle, hypotenuse (AC = PR = 10 cm), and one leg (AB = PQ = 6 cm) equal, satisfying RHS criterion.