CBSE Class 7 Mathematics Congruence of Lines and Angles Assignment Set 03

VII - Mathematics Assignment No-04 - Congruence of Triangles

Fill the gap in the following

Question 1. Two triangles are congruent if they are of the same shape and ..........
Answer: Same size
In simple words: Congruent triangles have identical shapes and equal sizes.

Exam Tip: Remember that congruence implies exact superimposition, meaning both shape and size must match.

Question 2. Two line segments are congruent, if they have ..........
Answer: Same length
In simple words: Two line segments are equal in length when they are congruent.

Exam Tip: Line segments only have one dimension (length), so equality of length determines congruence.

Question 3. Two angles are congruent if they have ..........
Answer: Same measure
In simple words: Two angles are congruent if their degree measures are equal.

Exam Tip: Always look at the degree measure when comparing the congruence of angles.

Question 4. Two triangles are congruent by .......... or .......... or ..........
Answer: SAS, SSS, ASA (or RHS)
In simple words: These are the standard criteria used to prove that two triangles are congruent.

Exam Tip: Memorize the four main congruence criteria: SSS, SAS, ASA, and RHS.

Question 5. Two rectangles are congruent if they have ..........
Answer: Same length and same breadth
In simple words: Rectangles need both identical lengths and identical widths to be congruent.

Question 6. Two circles are congruent if they have ..........
Answer: Same radius
In simple words: Circles with equal radii are identical in size and shape.

Exam Tip: The radius (or diameter) completely defines the size of a circle.

Question 7. Two squares are congruent if they have ..........
Answer: Same side length
In simple words: Squares are regular quadrilaterals, so one equal side length makes them congruent.

Exam Tip: Since all sides of a square are equal, knowing one side length is sufficient.

Question 8. If area of two triangles are equal then the triangles are ..........
Answer: Congruent (may or may not)
In simple words: Equal areas do not guarantee congruence, as shapes can differ while having the same area.

Exam Tip: Do not confuse equal area with congruence; area is a measure of 2D space, not shape.

Question 9. Congruent triangles have .......... Area
Answer: Equal
In simple words: Since congruent triangles are identical, their areas must also be equal.

Exam Tip: Congruence implies all corresponding parts (sides, angles, perimeter, area) are equal.

Question 10. If three angles of one triangle are equal to corresponding angles of another triangle then the triangles are ..........
Answer: not Congruent (necessarily, they are similar)
In simple words: AAA proves similarity, not congruence, because the triangles can be of different sizes.

Exam Tip: AAA (Angle-Angle-Angle) is a criterion for similarity, not congruence. Side lengths are needed for congruence.

Question 11. In an equilateral triangle, all angles .......... to one another
Answer: are equal
In simple words: All three internal angles of an equilateral triangle measure \(60^\circ\).

Exam Tip: Equilateral means equal sides and consequently equal angles.

Question 12. The bisector of the vertical angle of an isosceles triangle .......... the base at .......... angle.
Answer: Bisects, right
In simple words: The line dividing the vertex angle in an isosceles triangle cuts the base exactly in half at a \(90^\circ\) angle.

Exam Tip: In an isosceles triangle, the angle bisector of the vertex is also the median and altitude to the base.

Question 13. Among two congruent angles, one has a measure of \(70^\circ\), the measure of other angle is ..........
Answer: \(70^\circ\)
In simple words: Congruent angles have identical measures.

Exam Tip: Always apply the definition of congruence: corresponding parts of congruent figures are equal.

Question 14. When we write in any triangle \(\angle A = \angle B\), we actually mean ..........
Answer: \(m\angle A = m\angle B\)
In simple words: We mean that the numerical measure of angle A is equal to the numerical measure of angle B.

Exam Tip: Strictly speaking, geometric angles are figures, so equality between them refers to their numerical measures.

Question 15. In two right-angled triangles, if two legs of one \(\Delta\) are equal to corresponding two legs of other \(\Delta\) then the \(\Delta\)s are ..........
Answer: Congruent
In simple words: By the SAS criterion (since the included right angle is the same), the two right triangles are congruent.

Exam Tip: The two legs forming the right angle give the SAS condition automatically since the right angle is included.