geometry
name alex.d id: 1
geometry basics practice
date__________ period____
name each angle in four ways.
1)
diagram with f, g, h
choose the wrong name for this angle:
a) ∠gfh b) ∠g c) ∠fgh d) ∠5
2)
diagram with i, j, k
choose the wrong name for this angle:
a) ∠j b) ∠jki c) ∠i d) ∠ljk
name the vertex and sides of each angle.
3)
diagram with j, i, k
a) j, $\overline{ji}$ and $\overline{ik}$ b) j, $\overline{ji}$ and $\overline{jk}$ c) i, $\overline{ji}$ and $\overline{jk}$ d) k, $\overline{ji}$ and $\overline{jk}$
4)
diagram with e, d, f
a) f, $\overline{ed}$ and $\overline{ef}$ b) d, $\overline{ed}$ and $\overline{ef}$ c) e, $\overline{ed}$ and $\overline{ef}$ d) e, $\overline{ed}$ and $\overline{df}$
5)
diagram with h, g, f
a) g, $\overline{gf}$ and $\overline{fh}$ b) f, $\overline{fg}$ and $\overline{fh}$ c) h, $\overline{hg}$ and $\overline{hf}$ d) g, $\overline{gf}$ and $\overline{gh}$
6)
diagram with j, i, h
a) i, $\overline{ih}$ and $\overline{ij}$ b) i, $\overline{ih}$ and $\overline{hj}$ c) j, $\overline{ji}$ and $\overline{jh}$ d) h, $\overline{ih}$ and $\overline{ij}$
name all the angles that have v as a vertex.
7.
diagram with g, v, h, i
a) ∠1, ∠2, ∠hgv b) ∠1, ∠2, ∠ihg c) ∠1, ∠2, ∠vih d) ∠1, ∠2, ∠gvt
8.
diagram with v, h, j, i
a) ∠5, ∠6, ∠jih b) ∠5, ∠6, ∠ihv c) ∠5, ∠6, ∠vji d) ∠5, ∠6, ∠hvj

Question

Accepted Answer

### Question 1: Choose the wrong name for the angle
# Brief Explanations:
To name an angle, the vertex should be the middle letter when using three - letter notation. The angle at $G$ has sides $GF$ and $GH$.
- Option A: $\angle GFH$ has vertex $F$, which is not the vertex of the given angle (the angle is at $G$), so this is incorrect.
- Option B: $\angle G$ is a valid way to name the angle with vertex $G$.
- Option C: $\angle FGH$ has vertex $G$ (middle letter) and sides $FG$ and $GH$, which is correct.
- Option D: $\angle5$ is a valid way to name the angle (using the number at the vertex).

# Answer: A. $\angle GFH$

### Question 2: Choose the wrong name for the angle
# Brief Explanations:
The angle at $J$ has sides $JI$ and $JK$.
- Option A: $\angle J$ is a valid way to name the angle with vertex $J$.
- Option B: $\angle JKI$ has vertex $K$, which is not the vertex of the given angle (the angle is at $J$), so this is incorrect.
- Option C: $\angle I$ is incorrect? Wait, no. Wait, the angle at $J$, but if we consider the notation, $\angle I$ would have vertex $I$, but the angle is at $J$. Wait, no, let's re - examine. The angle is at $J$, with sides $JI$ and $JK$.
- Option D: $\angle IJK$ has vertex $J$ (middle letter) and sides $IJ$ (same as $JI$) and $JK$, which is correct. Wait, maybe I made a mistake. Let's start over. The angle is formed by $JI$ and $JK$ with vertex $J$.
- Option A: $\angle J$ is correct (vertex - only name).
- Option B: $\angle JKI$: The vertex here is $K$, so this is wrong.
- Option C: $\angle I$: The vertex is $I$, which is not the vertex of our angle (vertex is $J$), so $\angle I$ is also wrong? Wait, no, the question is to choose the wrong name. Wait, maybe the angle is at $J$, so the correct names should have $J$ as the vertex. $\angle J$ (A) is correct, $\angle JKI$ (B) has vertex $K$ (wrong), $\angle I$ (C) has vertex $I$ (wrong), $\angle IJK$ (D) has vertex $J$ (correct). But the options must have only one wrong? Wait, maybe I misread the diagram. Assuming the angle is at $J$, with sides $JI$ and $JK$. So $\angle J$ (A) is correct, $\angle JKI$ (B) is wrong (vertex $K$), $\angle I$ (C) is wrong (vertex $I$), $\angle IJK$ (D) is correct. But the problem says "Choose the wrong name", maybe there is a typo or my misinterpretation. Wait, maybe the angle is at $J$, and the sides are $JI$ and $JK$. So the correct three - letter names are $\angle IJK$ or $\angle KJI$. $\angle J$ is correct (vertex name). $\angle JKI$ has vertex $K$, so it's wrong. $\angle I$ has vertex $I$, wrong. $\angle IJK$ is correct. But the options are given as A) $\angle J$, B) $\angle JKI$, C) $\angle I$, D) $\angle IJK$. Wait, maybe the intended wrong one is B) $\angle JKI$ because its vertex is $K$ instead of $J$.

# Answer: B. $\angle JKI$

### Question 3: Name the vertex and sides of the angle
# Brief Explanations:
The angle is formed at point $J$, with one side along $JI$ and the other along $JK$.
- Option A: Sides $\overline{JI}$ and $\overline{IK}$ are wrong, because the other side is $JK$ not $IK$.
- Option B: Vertex $J$, sides $\overline{JI}$ and $\overline{JK}$ are correct.
- Option C: Vertex $I$ is wrong, the vertex is $J$.
- Option D: Vertex $K$ is wrong, the vertex is $J$.

# Answer: B. $J,\overline{JI}$ and $\overline{JK}$

### Question 4: Name the vertex and sides of the angle
# Brief Explanations:
The angle is formed at point $E$, with one side along $ED$ and the other along $EF$.
- Option A: Vertex $F$ is wrong, the vertex is $E$.
- Option B: Vertex $D$ is wrong, the vertex is $E$.
- Option C: Vertex $E$, sides $\overline{ED}$ and $\overline{EF}$ are correct.
- Option D: Side $\overline{DF}$ is wrong, the other side is $EF$ not $DF$.

# Answer: C. $E,\overline{ED}$ and $\overline{EF}$

### Question 5: Name the vertex and sides of the angle
# Brief Explanations:
The angle is formed at point $G$, with one side along $GF$ and the other along $GH$.
- Option A: Side $\overline{FH}$ is wrong, the other side is $GH$ not $FH$.
- Option B: Vertex $F$ is wrong, the vertex is $G$.
- Option C: Vertex $H$ is wrong, the vertex is $G$.
- Option D: Vertex $G$, sides $\overline{GF}$ and $\overline{GH}$ are correct.

# Answer: D. $G,\overline{GF}$ and $\overline{GH}$

### Question 6: Name the vertex and sides of the angle
# Brief Explanations:
The angle is formed at point $I$, with one side along $IH$ and the other along $IJ$.
- Option A: Vertex $I$, sides $\overline{IH}$ and $\overline{IJ}$ are correct.
- Option B: Side $\overline{HJ}$ is wrong, the other side is $IJ$ not $HJ$.
- Option C: Vertex $J$ is wrong, the vertex is $I$.
- Option D: Vertex $H$ is wrong, the vertex is $I$.

# Answer: A. $I,\overline{IH}$ and $\overline{IJ}$

### Question 7: Name all the angles that have $V$ as a vertex
# Brief Explanations:
The angles with vertex $V$ are $\angle1$ (between $GV$ and $VH$), $\angle2$ (between $VH$ and $VI$), and $\angle GVI$ (between $GV$ and $VI$).
- Option A: $\angle HGV$ has vertex $G$, wrong.
- Option B: $\angle IHG$ has vertex $H$, wrong.
- Option C: $\angle VIH$ has vertex $I$, wrong.
- Option D: $\angle1,\angle2,\angle GVI$ are all angles with vertex $V$, correct.

# Answer: D. $\angle1,\angle2,\angle GVI$

### Question 8: Name all the angles that have $V$ as a vertex
# Brief Explanations:
The angles with vertex $V$ are $\angle5$ (between $VH$ and $VI$), $\angle6$ (between $VJ$ and $VI$), and $\angle HVJ$ (between $VH$ and $VJ$).
- Option A: $\angle JIH$ has vertex $I$, wrong.
- Option B: $\angle IHV$ has vertex $H$, wrong.
- Option C: $\angle VJI$ has vertex $J$, wrong.
- Option D: $\angle5,\angle6,\angle HVJ$ are all angles with vertex $V$, correct.

# Answer: D. $\angle5,\angle6,\angle HVJ$

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Question 1: Choose the wrong name for the angle

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Question 2: Choose the wrong name for the angle