Questions On Congruence Of Triangles Class 7 Pdf

Questions On Congruence Of Triangles Class 7 Pdf

Understanding the congruence of triangles is an essential part of geometry in Class 7. Congruence means that two figures have the same shape and size. In the case of triangles, congruence can be determined using specific rules and criteria. This topic covers important questions, explanations, and exercises related to the congruence of triangles.

If you are looking for questions on congruence of triangles for Class 7 in PDF format, this topic provides detailed questions with answers, helping students strengthen their concepts in geometry.

What is Congruence of Triangles?

Two triangles are congruent if they have:

  • Equal corresponding sides
  • Equal corresponding angles

When two triangles are congruent, they have the same shape and size, even if one is rotated or flipped.

Criteria for Triangle Congruence

To prove two triangles are congruent, we use the following criteria:

1. SSS (Side-Side-Side) Criterion

If all three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.

2. SAS (Side-Angle-Side) Criterion

If two sides and the included angle of one triangle are equal to the two sides and the included angle of another triangle, then the triangles are congruent.

3. ASA (Angle-Side-Angle) Criterion

If two angles and the included side of one triangle are equal to the two angles and the included side of another triangle, then the triangles are congruent.

4. AAS (Angle-Angle-Side) Criterion

If two angles and any one non-included side of one triangle are equal to the corresponding two angles and one non-included side of another triangle, then the triangles are congruent.

5. RHS (Right Angle-Hypotenuse-Side) Criterion

If the hypotenuse and one side of a right-angled triangle are equal to the hypotenuse and one side of another right-angled triangle, then the two triangles are congruent.

Important Questions on Congruence of Triangles

Below are some important questions for Class 7 students to practice.

1. Multiple-Choice Questions (MCQs)

Q1: If two triangles are congruent, then which of the following is true?

  1. Their corresponding sides are equal
  2. Their corresponding angles are equal
  3. Both (a) and (b)
  4. None of these

Answer: c) Both (a) and (b)

Q2: Which of the following is not a criterion for triangle congruence?

  1. ASA
  2. SSA
  3. RHS
  4. SSS

Answer: b) SSA

Q3: In the SAS criterion, the angle should be:

  1. The included angle
  2. Any angle
  3. A right angle
  4. None of these

Answer: a) The included angle

2. Fill in the Blanks

  1. Two triangles are congruent if their __________ and __________ are equal.
    (Answer: corresponding sides, corresponding angles)

  2. The RHS criterion is applicable only for __________ triangles.
    (Answer: right-angled)

  3. In the ASA criterion, the side must be __________ by two angles.
    (Answer: included)

3. True or False Questions

  1. Two equilateral triangles of different sizes are congruent. (False)
  2. The SAS criterion requires two sides and an included angle. (True)
  3. The AAS criterion can be used when one side and two angles are given. (True)

Word Problems on Congruence of Triangles

Q1: Triangle Congruence in Real Life

A bridge has two identical triangular structures on both sides. If one triangular structure has sides 5 cm, 6 cm, and 7 cm, and the other has the same measurements, prove that the triangles are congruent.

Solution:
Since all three sides of one triangle are equal to the three sides of the other triangle, we use the SSS (Side-Side-Side) Criterion.
Thus, the triangles are congruent.

Q2: Finding the Missing Angle

In two triangles, two angles are given as 50° and 60°. The third angle is missing. Can you prove that the two triangles are congruent if one side is also equal?

Solution:

  • The sum of angles in a triangle is 180°.
  • The missing angle = 180° – (50° + 60°) = 70°.
  • Since two angles and one side are equal, we use the AAS (Angle-Angle-Side) Criterion.
  • Hence, the triangles are congruent.

Why is Triangle Congruence Important?

1. Used in Geometry

Congruence helps in understanding shapes, symmetry, and transformations.

2. Helps in Construction

Engineers and architects use congruent triangles to design bridges, buildings, and machines.

3. Essential for Higher Mathematics

Understanding triangle congruence is necessary for studying trigonometry and coordinate geometry.

Common Mistakes to Avoid

  1. Confusing SSA with congruence – SSA (Side-Side-Angle) is not a valid congruence criterion.
  2. Ignoring the included angle – In SAS and ASA, the angle must be between the given sides.
  3. Incorrect calculations – Always check angle sums to avoid mistakes.

Practice Questions for Students

  1. State the congruence criterion used for the following pairs of triangles:

      1. Two triangles with all sides equal.
      1. Two triangles with two sides and an included angle equal.
      1. Two triangles with two angles and one non-included side equal.

  2. Prove that two triangles with sides 3 cm, 4 cm, and 5 cm are congruent to another triangle with the same sides.

  3. If two triangles have angles 40°, 60°, and 80°, and one side equal, which congruence rule applies?

  4. Identify whether the following statements are true or false:

      1. The RHS rule applies to all triangles.
      1. The ASA rule requires an included side.
      1. The sum of angles in a triangle is 200°.

  5. Draw two congruent triangles and label their sides and angles. Explain why they are congruent.

The congruence of triangles is a fundamental concept in geometry, helping students understand how shapes and sizes remain consistent despite transformations. By mastering SSS, SAS, ASA, AAS, and RHS criteria, students can solve complex problems and apply them to real-life situations.

Practicing important questions and solving congruence exercises will improve logical thinking and problem-solving skills. Keep practicing and enjoy learning geometry!