Students will be expected to draw and measure an angle using the protractor and to develop skills and perform demonstrations using the properties on corresponding angles, opposite by vertex and alternate-internal or alternate-external angles and parallel lines in fifth grade. This course on corresponding, opposite and alternate-intercept angles as well as the position of two straight lines and the properties of angles in the fifth grade will help you progress further in geometry.

## I. Angle and parallelism

Definition:

Two angles are said to be adjacent if they have their vertex in common as well as a side in common and if they are located on either side of this side in common.

Example:

The angles and have as common vertex the point O, as common side the half-straight [OB) and they are placed on both sides of [OB): they are thus adjacent.

Remark:

Adjacent angles and share a flat angle. Their sum is therefore equal to 180°. They are said to be extra.

#### 2. Corresponding angles and alternate-internal angles

Definition:

The blue angles are alternating-internal, that is, they are determined by the lines (d), (d’) and the secant .

The green angles are corresponding. That is, they are determined by the lines (d), (d’) and the secant .

Ownership:

Two alternating-internal angles have the same measure if, and only if, the two lines cut by the secant are parallel.

Two corresponding angles have the same measure if, and only if, the two lines cut by the secant are parallel.

Example:

The angles and are alternating-internal because they are determined by the secant (BC) and the lines (AB) and (CD).

In addition, the coding indicates that they have the same measurement. Therefore the lines (AB) and (CD) are parallel.

Example:

We know that the lines (AB) and (CD) are parallel.

• The corresponding angles and are determined by the secant (AC) and the lines (AB) and (CD), parallel to each other. So they have the same measurement. So .
• The alternating-internal angles and are determined by the secant (BC) and the lines (AB) and (CD) , parallel to each other. So they have the same measurement. So .

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