# Congruence of Triangles

**Congruent Objects:** When two objects are exact copies of each other, they are called congruent.

Two line segments AB and CD are congruent when they have equal lengths.

Two angles are congruent if their measurement is equal.

## Congruence Criteria

#### SSS (Side Side Side) Congruence of two triangles:

When three sides of a triangle are equal to three corresponding sides of another triangle, the triangles are congruent.

#### SAS (Side Angle Side) Congruence of two triangles:

When two sides and the angle between them (in one triangle) are equal to corresponding sides and the angle between them (in another triangle), the triangles are congruent.

#### ASA (Angle Side Angle) Congruence of two triangles:

When two angles and a side between them (in one triangle) are equal to the corresponding angles and side between them (in another triangle), the triangles are congruent.

#### RHS Congruence of two right-angled triangles:

When the hypotenuse and one of the legs (of a right angled triangle) are equal to hypotenuse and one of the legs (of another right angled triangle), the triangles are congruent.

## Exercise 7.1

**Question 1:** Complete the following statements:

- Two line segments are congruent if ___________.
- Among two congruent angles, one has a measure of 70°, the measure of the other angle is ___________.
- When we write ÐA = ÐB, we actually mean ___________.

**Answer:**(a) their lengths are equal, (b) 70°, (c) equal length

**Question 2:** Give any two real-life examples for congruent shapes.

**Answer:** Two coins of 50 p and two coins of 1 rupee.

**Question 3:** If ΔABC ≈ ΔFED under the correspondence ABC ↔ FED, write all the corresponding congruent parts of the triangles.

**Answer:** AB = FE, BC = ED, AC = FD, angles A = F, B = E, and C = D

**Question 4:** If ΔDEF ≈ ΔBCA, write the part(s) of ΔBCA that correspond to (i) ∠E (ii) EF (iii) ÐF (iv) ∠F

**Answer:** (i) → ∠C, (ii) → CA, (iii) → BA, (iv) → ∠A