Congruency of Triangles

Congruent Triangles Properties and CPCT Rules

Congruent Triangles

Congruent Triangles are triangles that have an equivalent size and shape. This means that the corresponding sides are equal and therefore the corresponding angles are equal. In this article, we are going to discuss the congruence of triangles class 7 cbse.

It can be told whether two triangles are congruent without testing all the sides and all the angles of the two triangles. In this lesson, we'll consider the four rules to prove triangle congruence. It’s called the SSS rule, SAS rule, ASA rule, and AAS rule. In congruence of triangles class 7, we'll consider a symbol used for right triangles called the Hypotenuse Leg Rule.


Properties of Congruent Triangles

Now we know about the congruence of triangles class 7 CBSE. Let’s discuss the properties. If two triangles are congruent, then each part of the Triangulum (side or angle) is congruent to the corresponding part within the other triangle. This is the truth value of the concept; once you've proven two triangles are congruent, you'll find the angles or sides of 1 of them from the opposite .

To remember this important idea, we usually find it very helpful to use the acronym CPCTC, which is the short form for "Corresponding Parts of Congruent Triangles are Congruent".

In addition to sides and angles, all other properties of Triangulum are equivalent also, like area, perimeter, location of centers, circles, etc.


How Will You Know That a Triangle is Congruent?

We can prove the congruence of triangles for class 7 CBSE using a few ways. A triangle is basically defined by six measures (three sides, three angles). But you do not get to know all of them to point out that two triangles are congruent. Various groups of three will do. Triangles are congruent if:

  1. SSS (side side side)
    All three corresponding sides are equal in length.

  2. SAS (side angle side)
    A pair of corresponding sides and therefore the included angle are equal.

  3. ASA (angle side angle)
    A pair of corresponding angles and therefore the included side are equal.

  4. AAS (angle angle side)
    A pair of the corresponding angles and a non-included side is equal.

  5. HL (hypotenuse leg of a right triangle)
    Two right angled triangles are congruent only if the hypotenuse and one leg are the same.


CPCT Rules in Maths

The full sort of CPCT is corresponding parts of congruence of triangles class 7 CBSE. Congruency are often predicted without actually measuring the edges and angles of a triangle. Different rules of congruency are as follows.

  • SSS (Side-Side-Side)

  • SAS (Side-Angle-Side)

  • ASA (Angle-Side-Angle)

  • AAS (Angle-Angle-Side)

  • RHS (Right angle-Hypotenuse-Side)


Let Us Learn All Three Conditions of Congruence of Triangles Class 7 CBSE in Detail.

SSS (Side-Side-Side)

If all three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.


SAS (Side-Angle-Side)

If any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two other triangles are known to be congruent by SAS rule.


ASA (Angle-Side- Angle)

If any two angles and sides included between the angles of 1 triangle are like the corresponding two angles and side included between the angles of the second triangle, then the 2 triangles are said to be congruent by ASA rule.


AAS (Angle-Angle-Side)

AAS stands for Angle-angle-side. When two angles and a non-included side of a triangle are adequate to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

Students many times get confused for AAS with ASA congruency. But remember that AAS is for the non-included side, whereas ASA is for included sides of the triangles.


RHS (Right Angle-Hypotenuse-Side)

If the hypotenuse and a side of a right-angled triangle are equivalent to the hypotenuse and a side of the second right-angled triangle, then the two right triangles are said to be congruent by RHS rule.


Information You Need to Check Whether the Triangles Are Congruent or Not

Let us draw a congruent triangle for ΔABC. You can do so if you've got the subsequent information:

  • The lengths of all of the three sides of ΔABC OR

  • The length of two sides are therefore the angle between them OR

  • The measure of the two angles and length of their side included by them.

Important Observations: Two angles are said to be congruent whenever they have the same measurement. Instead of denoting congruence by ≅ you can also denote it by = since they are equal in measure.

FAQs (Frequently Asked Questions)

1. What is Congruence?

Congruence is the term used to define an object and its mirror image. Two objects or shapes are said to be congruent if they superimpose on one another . Their shape and dimensions are the same. In the case of geometric figures, line segments with an equivalent length are congruent and angles with an equivalent measure are congruent.

2. How is congruence applied in real life?

Whenever an object is kept in front of the mirror, that mirror image is found to be congruent to the real image. Whenever two objects are said to be congruent then all of the corresponding angles and sides are also congruent. Real-life examples are, cigarettes in a packet are congruent to one another.

3. What does congruent mean?

In geometry, two of the figures are congruent only if they need an equivalent shape and size, or if one of them has an equivalent shape and size because of the reflection of the other. This suggests that either objects are often repositioned and reflected (but not resized) precisely with the opposite object.

4. Does SSS prove congruence?

SSS Postulate (Side-Side-Side)

If three sides of 1 triangle are congruent to 3 sides of another triangle, then the triangles are congruent. As you'll see, the SSS Postulate doesn't concern itself with angles in the least .