Question

name:
2.4 - 2.5 review
geometry: mr. mill
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. ∠hca

a) b) c)

1. ∠8

a) b) c)

1. ∠fgh

a) b) c)

Explanation:

1) For \(\angle HCA\)

a) Another name

An angle can be named by its vertex if there is only one angle at that vertex. But here, using three - letter notation (vertex in the middle), another name could be \(\angle 2\) (assuming the numbering in the diagram corresponds to the angle measure).

b) Vertex

The vertex of an angle named \(\angle HCA\) is the middle letter. So the vertex is \(C\).

c) Sides

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

2) For \(\angle 8\)

a) Another name

Using three - letter notation (vertex in the middle). If we assume the vertex is \(G\) (from the diagram structure), another name is \(\angle JGH\)

b) Vertex

The vertex of \(\angle 8\) (assuming the standard angle - naming where the vertex is the common point of the two rays forming the angle) is \(G\)

c) Sides

The sides of \(\angle 8\) are \(\overrightarrow{GJ}\) and \(\overrightarrow{GH}\)

3) For \(\angle FGH\)

a) Another name

Using the numbering in the diagram (assuming a consistent numbering system for angles), another name could be \(\angle 9\)

b) Vertex

The vertex of an angle named \(\angle FGH\) is the middle letter. So the vertex is \(G\)

c) Sides

The sides of an angle named \(\angle FGH\) are \(\overrightarrow{GF}\) and \(\overrightarrow{GH}\)

Answer:

1)
a) \(\angle 2\)
b) \(C\)
c) \(\overrightarrow{CH}\) and \(\overrightarrow{CA}\)

2)
a) \(\angle JGH\)
b) \(G\)
c) \(\overrightarrow{GJ}\) and \(\overrightarrow{GH}\)

3)
a) \(\angle 9\)
b) \(G\)
c) \(\overrightarrow{GF}\) and \(\overrightarrow{GH}\)