# Angle Side Angle Postulate

Proving Congruent Triangles With ASA

### Example of Angle Side Angle Proof

$$\triangle$$ABC $$\cong$$ $$\triangle$$XYZ

• Two angles and the included side are congruent
• $$\angle$$CAB = $$\angle$$ZXY (angle)
• AB = XY  (side)
• $$\angle$$ACB = $$\angle$$XZY  (angle)
• Therefore, by the Angle Side Angle postulate (ASA), the triangles are congruent.

### Included Side

The included side means the side between two angles. In other words it is the side 'included between' two angles.

Identify Angle Side Angle Relationships

In which pair of triangles pictured below could you use the Angle Side Angle postulate (ASA) to prove the triangles are congruent?

### Practice Proofs

##### Proof 1

Prove that $$\triangle LMO \cong \triangle NMO$$

##### Proof 2

Use the ASA postulate to that $$\triangle ACB \cong \triangle DCB$$

##### Proof 3

Use the ASA postulate to that $$\triangle ABD \cong \triangle CBD$$

We can use the Angle Side Angle postulate to prove that the opposite sides and the opposite angles of a parallelogram are congruent

##### Proof 4

Given: ABCD is a parallelogram.

Prove the opposite sides and the opposite angles of a parallelogram are congruent.

Remember the definition of parallelogram: a quadrilateral that has two pairs of opposite parallel sides.