**Congruence of Triangles**

This worksheet is for **Grade 7 maths**, comprising the topic of** Congruence of Triangles**. It will help students develop a better understanding of Congruence of Triangles.

Upon the completion of this worksheet, students would be easily able to comprehend the following:

- Define Congruent Triangles
- What does CPCT stands for?
- Explain the rules of congruency.

**1.Define Congruent Triangles.**

Two triangles are referred to as congruent, if their three sides as well as three angles are equivalent in any orientation. Congruence is depicted by the symbol ‘⩭’.

**2.What does CPCT stands for?**

Corresponding parts of congruent triangles is abbreviated as CPCT. The CPCT theorem asserts that if two or more congruent triangles are selected, the corresponding angles and sides of the triangles are also congruent to each other.

**3. Explain the rules of congruency.**

Five main rules of congruency for triangles are as follows:

**Side-Side-Side (or SSS):**

The two triangles are said to be congruent by SSS rule, if all three sides of one triangle are comparable to the corresponding three sides of the second triangle.

For example, in the image above, AB is comparable to PQ, AC is comparable to PR and CB is comparable to QR.

**Side-Angle-Side (or SAS):**

The two triangles are said to be congruent by SAS rule, if any two sides and angle contained between the sides of one triangle are comparable to the corresponding two sides and angle between second triangle sides.

For example, in the image above, AB is comparable to PQ, AC is comparable to PR and the angle between AB & AC, Angle CAB is comparable to the angle between PQ & PR, Angle RPQ.

**Angle-Side-Angle (or ASA):**

The two triangles are said to be congruent by ASA rule, if any two angles and sides included between the angles of one triangle are comparable to the corresponding two angles and sides included between the second triangle angles.

For example, in the image above, Angle ACB is comparable to Angle PRQ, Angle ABC is comparable to Angle PQR and the sides between both these angles in both these triangles, CB and QR are comparable.

**Angle-Angle-Side (or AAS):**

According to this rule, congruent triangles have two angles and a non-included side that are equal.

AAS is similar to ASA wherein 2 angles and 1 side in 2 different triangles are comparable.

**Right angle- Hypotenuse-Side( or RHS): **

**RHS congruence rule** : The two right triangles are said to be congruent by the **RHS rule** if the hypotenuse and a side of one right-angled triangle are comparable to the hypotenuse and a side of the other right-angled triangle.

For example, in the above image, XZ and RT are congruent, YZ and ST are congruent, and Angles XYZ and Angle RST are congruent.

**Answer for the Above Worksheet**

Download Congruence of triangles class 7 PDF Worksheet

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