Multiple Choice Questions (MCQs) are an effective way to assess understanding and reinforce concepts, especially in mathematics like the congruence of triangles. For Class 7 students, understanding the principles of congruencewhen two triangles are identical in shape and sizeis crucial for foundational geometry. This article presents a series of MCQs designed to test and enhance your knowledge of congruence of triangles, covering key concepts and their applications.
MCQs on Basic Concepts of Congruence
- Question: Two triangles are congruent if:
- A) Their corresponding sides are proportional.
- B) Their corresponding angles are equal.
- C) Their corresponding sides and angles are equal.
- D) They have the same perimeter.
Answer: B) Their corresponding angles are equal.
Explanation: Congruent triangles have exactly the same size and shape. This means that all corresponding angles and sides are equal.
- Question: Which of the following conditions is NOT sufficient to prove the congruence of two triangles?
- A) SAS (Side-Angle-Side)
- B) AAA (Angle-Angle-Angle)
- C) SSS (Side-Side-Side)
- D) ASA (Angle-Side-Angle)
Answer: B) AAA (Angle-Angle-Angle)
Explanation: AAA is not a sufficient condition to prove congruence because two triangles with the same angles may have different sizes.
- Question: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent by:
- A) SAS Criterion
- B) ASA Criterion
- C) SSS Criterion
- D) RHS Criterion
Answer: A) SAS Criterion
Explanation: SAS (Side-Angle-Side) criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
MCQs on Properties and Applications of Congruence
- Question: In a triangle ABC, if AB = AC and ?B = ?C, then triangle ABC is:
- A) Isosceles
- B) Scalene
- C) Equilateral
- D) None of the above
Answer: A) Isosceles
Explanation: An isosceles triangle has at least two sides of equal length. Here, AB = AC makes triangle ABC isosceles.
- Question: If in two triangles, corresponding angles are equal and their corresponding sides are proportional, then the triangles are:
- A) Similar
- B) Congruent
- C) Identical
- D) Equilateral
Answer: A) Similar
Explanation: Similar triangles have equal corresponding angles and proportional corresponding sides, but they may not be identical in size.
- Question: The number of criteria needed to prove the congruence of two triangles are:
- A) 2
- B) 3
- C) 4
- D) 1
Answer: B) 3
Explanation: Three criteriaSSS, SAS, and ASAare sufficient to prove the congruence of two triangles. Each criterion involves matching corresponding sides and angles in different combinations.
MCQs on Practical Applications and Problem Solving
- Question: In triangle PQR, if PQ = 5 cm, QR = 7 cm, and PR = 6 cm, what type of triangle is PQR?
- A) Scalene
- B) Isosceles
- C) Equilateral
- D) Right-angled
Answer: A) Scalene
Explanation: A scalene triangle has all sides of different lengths. Here, PQ, QR, and PR are all different lengths.
- Question: If triangle ABC is congruent to triangle DEF by the SAS criterion, and AB = 4 cm, BC = 5 cm, and ?A = 90°, then triangle DEF must have:
- A) AB = 4 cm, BC = 5 cm, and ?D = 90°
- B) DE = 4 cm, EF = 5 cm, and ?D = 90°
- C) DE = 5 cm, EF = 4 cm, and ?E = 90°
- D) None of the above
Answer: B) DE = 4 cm, EF = 5 cm, and ?D = 90°
Explanation: By SAS criterion, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then they are congruent.
Mastering MCQs on the congruence of triangles is essential for Class 7 students to build a solid foundation in geometry. These questions not only test your understanding of the criteria for triangle congruence but also reinforce practical applications and problem-solving skills. By practicing these MCQs, students can enhance their knowledge and confidence in geometry, preparing them for more advanced concepts in mathematics.