CBSE Class 7 Mathematics Congruence of Lines and Angles Assignment Set 01

Mathematics Assignment No. 03 - Congruence of Triangles

Write True (T) or False (F) against the following statements.

Question 1. Two triangles are congruent if they are of the same shapes
Answer: False (F).
In simple words: Having the same shape is only similarity, not congruence. Congruent figures must also have the exact same size.

Exam Tip: Remember that similarity requires same shape, while congruence requires both same shape and same size.

Question 2. Two figures are said to be congruent figures if they are of the same shape and same size.
Answer: True (T).
In simple words: Two geometric figures are congruent if they can superimpose each other completely, meaning they match in both shape and size.

Exam Tip: This is the fundamental definition of congruence for any geometric figure.

Question 3. Two triangles are congruent if all the three angles of one triangle are equal to all the three angles of another triangle.
Answer: False (F).
In simple words: Equal angles guarantee that triangles are similar (AAA criterion), but not necessarily congruent, because their sides can be of different lengths.

Exam Tip: AAA (Angle-Angle-Angle) is a similarity criterion, never a congruence criterion.

Question 4. Two triangles are congruent if two sides and one angle of one triangle are equal to two sides and one angle of another triangle.
Answer: False (F).
In simple words: For triangles to be congruent by side-angle-side (SAS), the given angle must be the included angle between the two specified sides.

Exam Tip: SSA or ASS is not a valid congruence rule unless the angle is strictly the included angle.

Question 5. Two triangles are congruent if two angles and one side of one triangle is equal to two angles and one side of another triangle.
Answer: True (T).
In simple words: This is valid under the AAS (Angle-Angle-Side) or ASA (Angle-Side-Angle) congruence criteria since two angles automatically determine the third angle.

Question 6. Two rectangles are congruent, if they have the same length and the same breadth
Answer: True (T).
In simple words: Since rectangles are fully determined by their length and breadth, equal dimensions mean identical figures.

Exam Tip: For polygons with fixed right angles like rectangles, equal dimensions imply congruence.

Question 7. Two circles are congruent if they have the same radius.
Answer: True (T).
In simple words: Circles depend only on their radius; equal radii mean the circles are identical in size and shape.

Exam Tip: Radius is the single defining parameter for the congruence of circles.

Question 8. Two angles are congruent, if they have the same measure
Answer: True (T).
In simple words: Two angles with equal degree measures can be placed exactly over one another.

Exam Tip: Angle measure alone determines the congruence of angles.

Question 9. Two line segments are congruent if they have the same direction
Answer: False (F).
In simple words: Congruence of line segments depends entirely on their lengths, not on the direction in which they are oriented.

Exam Tip: Direction or orientation has no effect on line segment congruence; only length matters.

Question 10. AAA is a congruency rule.
Answer: False (F).
In simple words: AAA only proves similarity, not congruence, because triangles of different sizes can have the exact same angles.

Exam Tip: Valid triangle congruence rules are SSS, SAS, ASA, AAS, and RHS.

Question 11. AAS is a congruency rule.
Answer: True (T).
In simple words: Angle-Angle-Side is a valid criterion for triangle congruence.

Exam Tip: AAS is a direct corollary of the ASA congruence criterion.

Question 12. If the legs of a right triangle are equal to the legs of another right triangle, then the triangles are congruent.
Answer: True (T).
In simple words: This is essentially the SAS criterion, where the included right angle is the same in both triangles.

Exam Tip: Equal legs in right triangles imply SAS congruence since the angle between the legs is always \(90^\circ\).

Question 13. If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle, then the triangles are congruent.
Answer: False (F).
In simple words: Having equal hypotenuses is not enough; one more side or one acute angle must also be equal (RHS criterion).

Exam Tip: RHS requires both the hypotenuse and one side to be equal, not just the hypotenuse.

Question 14. In an isosceles triangle, the angles opposite to equal sides are equal.
Answer: True (T).
In simple words: The base angles of an isosceles triangle are always equal.

Exam Tip: This theorem is fundamental for solving geometry problems involving isosceles triangles.

Question 15. Two congruent figures are equal in area
Answer: True (T).
In simple words: Since congruent figures are identical in shape and size, they must occupy the exact same amount of space (area).

Exam Tip: Congruence always implies equal area, but equal area does not necessarily imply congruence.

Question 16. If the area of two figures are equal then the figures are congruent.
Answer: False (F).
In simple words: A rectangle and a square can have the exact same area without being congruent or having the same shape.

Exam Tip: Equal area is a necessary condition for congruence in some contexts, but it is not sufficient by itself.

Question 17. All Squares are congruent.
Answer: False (F).
In simple words: Squares have the same shape, but their sizes can vary (e.g., a square of side 2 cm and a square of side 5 cm are not congruent).

Exam Tip: All squares are similar, but they are congruent only if their side lengths are equal.

Question 18. If two squares have equal areas, they are congruent.
Answer: True (T).
In simple words: If two squares have equal areas, their side lengths must be equal, making them congruent.

Exam Tip: Area of square = \(\text{side}^2\). Equal area means equal sides.

Question 19. If two triangles are congruent then their corresponding sides are congruent and their corresponding angles are congruent.
Answer: True (T).
In simple words: Often abbreviated as CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

Exam Tip: This is the key property used in almost all triangle congruence proofs.

Question 20. The bisector of the vertical angle of an isosceles triangle bisects the base at right angles.
Answer: True (T).
In simple words: In an isosceles triangle, the line drawn from the vertex angle to the midpoint of the base is also perpendicular to the base.

Exam Tip: This property creates two congruent right triangles by RHS or SAS.