Congruent sides are the concept used in geometry when the sides of a figure are equal to each other. It could be two or three sides equal to each other. The word congruent or congruency means exactly equal in shape and size, irrespective of flipping or rotating a shape. Congruent sides can be seen in various geometric shapes such as triangles and quadrilaterals. In this article, we are going to learn more about congruent sides and solve a few examples to understand the concept better.
| 1. | What are Congruent Sides? |
| 2. | Congruent Sides in Triangles |
| 3. | Congruent Sides in Quadrilaterals |
| 4. | FAQs on Congruent Sides |
What are Congruent Sides?
Congruent sides also referred to as congruent line segments mean when the sides or line segments of a geometric shape or figure are equal to each other. We can see congruent sides in different shapes such as triangles and quadrilaterals. The congruency of any figure depends on both the sides and the angles.
Congruent Sides in Triangles
Triangles are best classified depending on the number of congruent sides a triangle has. The measurement or length of a triangle defines the properties of a triangle. There are three kinds of triangles that can be classified based on their sides, they are equilateral triangle, isosceles triangle, and scalene triangle. Let us look at all three briefly.
Isosceles Triangle
An isosceles triangle is a type of triangle where two sides or legs are equal or congruent to each other. The angle between these legs or sides are is called a vertex angle. The isosceles triangle theorem states that if two sides of a triangle are congruent, then the angles opposite to the congruent sides are also congruent. Conversely, if the two angles of a triangle are congruent, the corresponding sides are also congruent.
Equilateral Triangle
An equilateral triangle is a triangle in which all three sides are equal along with the angles being equal. The value of each angle of an equilateral triangle is 60 degrees therefore, it is also known as an equiangular triangle. The equilateral triangle is considered as a regular polygon or a regular triangle as angles are equal and sides are also equal.
Scalene Triangle
A scalene triangle is a triangle with all three sides of different lengths, and all three angles of different measurements. However, the different measurements don't affect the sum of all the interior angles of the scalene triangle. The sum of the three interior angles always adds up to 180 degrees, which satisfies the angle sum property of the triangle.
Congruent Sides in Quadrilaterals
A quadrilateral is a closed shape polygon obtained by joining four points among which any three points are non-collinear. The 2D shape consists of four sides, four vertices, and four angles. The different types of quadrilaterals have different properties and congruent sides, let's see what they are:
- Parallelogram: Opposite angles and pairs are congruent.
- Rectangle: Opposite sides are congruent along with the diagonals being equal.
- Square: All four sides are congruent.
- Rhombus: All four sides are congruent along with opposite angles being equal.
- Isosceles Trapezium: The two non-parallel opposite sides are congruent.
- Kite: The adjacent sides are congruent which makes it two pairs of adjacent sides are equal.
Related Topics
Listed below are a few interesting topics related to the congruent sides, take a look.
- Congruent Angles
- Congruence in Triangles
- Congruent Lines
Examples on Congruent Sides
Example 1: Emma has four squares with the following side lengths: Square A, side = 6 inches, Square B, side = 8 inches, Square C, side = 5 inches, Square D, side = 8 inches. She wants two squares that can be placed exactly one over the other. Can you help her choose the congruent squares?
Solution: Squares with the same sides will superimpose on each other because they will be congruent. So, Emma should find two squares whose side lengths are exactly the same. In the given list, we can see that Square B and Square D have sides of the same length, that is, 8 inches. Therefore, Emma can choose Square B and D because they can be placed exactly one over the other.
Example 2: Out of a parallelogram and rhombus, which geometrical figure will have all sides as congruent segments?
Solution: A parallelogram is a quadrilateral with opposite sides to be equal whereas, in a rhombus all the sides are equal. Thus, we can say that out of a parallelogram and a rhombus, a rhombus will have all its sides as congruent line segments.
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Practice Questions on Congruent Sides
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FAQs on Congruent Sides
What is Meant by Congruent Sides?
Congruent sides mean when the line segment of the triangles or the radii of two circles are of the same length and are equal to each other. Congruent sides can be seen in different geometric shapes such as triangles, quadrilaterals, and circles.
What Shapes are Congruent Sides?
There are different shapes or figures that consist of congruent sides. Line segments that have the same length are considered congruent sides. Two triangles with the sides measuring the same length are considered as congruent as the sides are equal. Various quadrilaterals such as rhombus, rectangle, parallelogram, etc have congruent sides where either the opposite sides are equal or all the sides are equal.
How Do You Find Congruent Sides?
If in any shape, the sides are of equal lengths they are known as congruent sides. For example, if two triangles have all three sides of the same length that are equal to each other, we can say that the triangles are congruent. This congruence rule is called SSS(side-side-side).
Which Triangles are Classified Based on Congruent Sides?
Triangles can be classified based on their sides and there are three triangles that come under this classification. They are:
- Equilateral Triangle: Where all three sides of the triangle are equal to each other i.e. the length of the sides measures the same.
- Isosceles Triangle: Where two sides or legs of the triangles are equal to each other.
- Scalene Triangle: The sides of a scalene triangle are not equal to each other.
Does a Square have 4 Congruent Sides?
Yes, a square has 4 sides that are equal to each other in measurement along with 4 right angles. A square is both a rhombus and a rectangle.
What are Congruent Sides Angles?
Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure. These are known as congruent sides angles.
Are All Rhombus Sides Congruent?
Yes, all the sides of a rhombus are congruent since the opposite sides of the shape are equal in length.
Are All Rectangle Sides Congruent?
Yes, all rectangles have congruent sides since it is a quadrilateral with 4 equal sides along with being a parallelogram with two pairs being parallel.
