**TOPIC 5: CONGRUENCE ~ MATHEMATICS FORM 2**

**TOPIC 5: CONGRUENCE ~ MATHEMATICS FORM 2**

**Congruence**

I’m sure you have seen some of the figure which in one way or another one of the shape can become another using turns, flip or slide.

These shapes are said to be Congruent.

Study this notes carefully to know different ways that can help you to recognize congruent figures.

**Note that**;

Two line segments are Congruent if they have the same length.

Two angles are Congruent if they have the same measure.

Two circles are Congruent if they have the same diameter.

**Properties of vertical angles**

They are Congruent: vertical angles are always of equal measure i.e. a = b, and c = d.

Sum of vertical angles (all four angles) is 360^{0} i.e. a + b + c + d =360^{0}

Sum of Adjacent angles (angles from each pair) is 180^{0} i.e. a + d =180^{0} ; a + c =180^{0} ; c + b =180^{0} ; b + d =180^{0}.

**≅**

**The following are conditions for two Triangles to be Congruent**:

SSS

(side-Side-Side): if three pairs of sides of two Triangles are equal in

length, then the Triangles are Congruent. Consider example below

showing two Triangles with equal lengths of the corresponding sides.

SAS

(Side-Angle-Side): This means that we have two Triangles where we know

two sides and the included angles are equal. For example;

the two sides and the included angle of one Triangle are equal to

corresponding sides and the included angle of the other Triangle, we say

that the two Triangles are Congruent.

ASA

(Angle- Side-Angle): If two angles and the included side of one

Triangle are equal to the two angles and included side of another

Triangle we say that the two Triangles are congruence. For example

AAS

(Angle-Angle-Side): If two angles and non included side of one triangle

are equal to the corresponding angles and non included side of the

other Triangle, then the two triangles are congruent. For example

HL

(hypotenuse-Leg): This is applicable only to a right angled triangle.

The longest side of a right angled triangle is called hypotenuse and the

other two sides are legs.

The same length of hypotenuse and

The same length for one of the other two legs.

the hypotenuse and one leg of one right angled triangle are equal to a

corresponding hypotenuse and one leg of the other right angled triangle,

the two triangles are congruent.

note: Do not use AAA (Angle-Angle-Angle). This means we are given all

three angles of a triangle but no sides. This is not enough information

to decide whether the two triangles are congruent or not because the

illustration below:

**Isosceles Triangle Theorem**

isosceles triangle has two congruent sides (opposite sides) and two

congruent angles.

other angle is called vertex angle.

and angle C is the vertex angle.

**The base angle Theorem**

In the isosceles triangle ABC, BA and BC are congruent. D and E are

points on AC such that AD is congruent to BD and BE is congruent to BC.

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