Question

part 1 - (a) write another name for each angle, (b) name its vertex, and (c) name its sides. you must use the correct notation.

1. \\( \angle b c a \\)

a) b) c)

1. \\( \angle 6 \\)

a) b) c)

1. \\( \angle e d j \\)

a) b) c)

Explanation:

1) For \(\angle BCA\)

a) Another name

An angle can be named by its vertex when there is only one angle at that vertex. Here, since the vertex is \(C\), another name is \(\angle C\).

b) Vertex

The vertex of an angle is the common endpoint of its sides. For \(\angle BCA\), the vertex is \(C\).

c) Sides

The sides of an angle are the two rays that form the angle. For \(\angle BCA\), the sides are \(\overrightarrow{CB}\) and \(\overrightarrow{CA}\).

2) For \(\angle6\)

a) Another name

We can name the angle using three - letter notation. The angle \(\angle6\) has vertex \(G\). So, another name is \(\angle FGH\) (assuming the rays forming the angle are \(\overrightarrow{GF}\) and \(\overrightarrow{GH}\)).

b) Vertex

The vertex of \(\angle6\) is \(G\) (as it is the common point of the rays forming the angle).

c) Sides

The sides of \(\angle6\) are \(\overrightarrow{GF}\) and \(\overrightarrow{GH}\) (the two rays that meet at vertex \(G\) to form the angle).

3) For \(\angle EDJ\)

a) Another name

We can also name the angle as \(\angle JDE\) (using the vertex \(D\) and the two other points on the rays of the angle).

b) Vertex

The vertex of \(\angle EDJ\) is \(D\) (the common endpoint of the rays \(\overrightarrow{DE}\) and \(\overrightarrow{DJ}\)).

c) Sides

The sides of \(\angle EDJ\) are \(\overrightarrow{DE}\) and \(\overrightarrow{DJ}\) (the two rays that form the angle at vertex \(D\)).

Answer:

1.

• a) \(\angle C\)
• b) \(C\)
• c) \(\overrightarrow{CB},\overrightarrow{CA}\)

2.

• a) \(\angle FGH\)
• b) \(G\)
• c) \(\overrightarrow{GF},\overrightarrow{GH}\)

3.

• a) \(\angle JDE\)
• b) \(D\)
• c) \(\overrightarrow{DE},\overrightarrow{DJ}\)