Solving Problems On Congruency
Example 1: ABCD is a square, where AC is diagonal. Prove that triangle, ABC and CDA are congruent?
Solution:
ABCD is a square, so all four sides are congruent. By the properties of square, we also know each angle formed by square is 90°.
Hence we have,
AB = CD
BC = DA
Also, Both Triangles have one side common i.e. AC,
By SSS Congruence theorem. Both triangles, ABC and CDA are congruent.
Example 2: Check whether the given Quadrilaterals are congruent or not.
Solution:
In the figure ABCD,
∠ABC = 90
But In PQRS
∠PQR ≠ 90
Hence, the angles of first quadrilateral are not equal to the angles of second quadrilateral. Therefore, the above given figures are not congruent to each other.
Congruency
Congruency is a mathematical term that means two or more objects have the same shape and size or if one is the mirror image of the other.
In this article, we will understand the basic geometric concept of congruency, how they are related, their types, some practical applications of congruency, and solve some problems in trigonometry.
Table of Content
- What is Congruency?
- Type of Congruency
- Properties and Characteristics of Congruent Figures
- Congruent and Similar Figure
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