Q1: What is the term used to describe the relationship between two objects that have exactly the same shape and size? (a) Similarity (b) Congruence (c) Equality (d) Symmetry
Solution:
Ans: (b) Congruence is the relation between two objects that are of exactly the same shape and size, as stated in the definition of congruent figures.
Q2: In the SSS congruence criterion, what does SSS stand for? (a) Side-Side-Side (b) Shape-Size-Side (c) Side-Shape-Size (d) Similar-Side-Side
Solution:
Ans: (a) SSS stands for Side-Side-Side, which is the criterion stating that triangles are congruent if all three sides of one triangle equal the corresponding sides of another.
Q3: Which congruence criterion specifically applies only to right-angled triangles? (a) SSS criterion (b) ASA criterion (c) SAS criterion (d) RHS criterion
Solution:
Ans: (d) The RHS (Right angle-Hypotenuse-Side) criterion is specifically designed for right-angled triangles, requiring equality of hypotenuse and one side between the two triangles.
Q4: What method can be used to examine the congruence of plane figures, line segments and angles? (a) Method of calculation (b) Method of superposition (c) Method of measurement (d) Method of construction
Solution:
Ans: (b) The method of superposition examines congruence by placing one figure over another to check if they cover each other exactly without twisting or stretching.
Q5: In the SAS congruence criterion, what does the 'A' represent? (a) Any side of the triangle (b) Area of the triangle (c) Included angle between two sides (d) Adjacent angle to a side
Solution:
Ans: (c) In SAS, the 'A' represents the included angle, which is the angle formed between the two sides that are being considered for the congruence criterion.
Fill in the Blanks
Q1: Two plane figures are congruent if each, when superimposed on the other, covers it _____.
Solution:
Ans: exactly
Q2: If two line segments are congruent, then they have the same _____.
Solution:
Ans: length
Q3: A plane figure is any shape that can be drawn in _____ dimensions.
Solution:
Ans: two
Q4: The symbol used to denote congruence is _____.
Solution:
Ans: ≅
Q5: There are _____ axioms used to determine if two triangles are congruent.
Solution:
Ans: 4
True or False
Q1: If two angles are congruent, then the lengths of their arms must be equal.
Solution:
Ans: False Two angles are congruent if they have the same measure, and the lengths of their arms do not matter for congruence.
Q2: Two triangles are congruent if all the sides and all the angles of one triangle are equal to the corresponding sides and angles of the other triangle.
Solution:
Ans: True This is the general definition of congruent triangles, where all six elements (three sides and three angles) must be equal between the triangles.
Q3: The ASA congruence criterion requires three angles of one triangle to equal three angles of another triangle.
Solution:
Ans: False ASA criterion requires two angles and the included side between them to be equal, not three angles, for triangles to be congruent.
Q4: When checking congruence using superposition, you should not twist, bend or stretch the traced or cut image.
Solution:
Ans: True To properly check congruence using superposition, the figure must not be twisted, bent or stretched, maintaining its original shape and size exactly.
Q5: If two line segments have equal lengths, they are congruent.
Solution:
Ans: True Two line segments are congruent if they have the same or equal length, which is the definition of congruence for line segments.
Match the Following
Column A
Column B
1. SSS congruence criterion
A. Two angles and the included side are equal
2. SAS congruence criterion
B. Any shape drawn in two dimensions
3. ASA congruence criterion
C. Hypotenuse and a side are equal in right triangles
4. RHS congruence criterion
D. Three sides of one triangle equal three sides of another
5. Plane figure
E. Two sides and the included angle are equal
Solution:
Ans:
1 - D: SSS criterion states that triangles are congruent when all three sides of one triangle equal the corresponding three sides of another.
2 - E: SAS criterion requires two sides and the included angle between them to be equal for triangle congruence to be established.
3 - A: ASA criterion requires two angles and the included side between them to be equal for establishing congruence between two triangles.
4 - C: RHS criterion applies to right-angled triangles where the hypotenuse and one side must be equal for congruence to be confirmed.
5 - B: A plane figure is defined as any shape that can be drawn in two dimensions, such as triangles, rectangles and squares.
Short Answer Questions
Q1: What are congruent objects and how is congruence examined using the method of superposition?
Solution:
Ans: Two objects are congruent if they have exactly the same shape and size. The method of superposition examines congruence by placing one figure over another. If the figures cover each other exactly when superimposed, they are congruent. This can be done by making a traced copy or cutting out one figure and placing it over the other without twisting, bending or stretching it.
Q2: Explain the SSS congruence criterion for triangles.
Solution:
Ans: The SSS (Side-Side-Side) congruence criterion states that two triangles are congruent if all three sides of one triangle are equal to the three corresponding sides of the other triangle. This means if the lengths of all three pairs of corresponding sides match exactly, the triangles are congruent. No angle measurements are needed for this criterion, only side lengths are compared.
Q3: What is the SAS congruence criterion and what does 'included angle' mean?
Solution:
Ans: The SAS (Side-Angle-Side) congruence criterion states that two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of the other triangle. The included angle is the angle formed between the two sides being considered. This angle must lie between the two equal sides for the criterion to apply correctly.
Q4: Describe what plane figures are and give examples of them.
Solution:
Ans: A plane figure is any shape that can be drawn in two dimensions. These figures lie flat on a plane surface and have only length and width, without any thickness. Common examples of plane figures include rectangles, squares, triangles, and rhombuses. All these shapes can be completely represented on a flat surface like paper and are studied in geometry.
Q5: How do we determine if two angles are congruent, and does the length of their arms matter?
Solution:
Ans: Two angles are congruent if they have the same measure. If two angles are congruent, their measures are the same. The lengths of the arms of the angles do not matter for congruence. Only the measure of the angle, which is the amount of rotation between the two arms, determines whether angles are congruent or not.
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