Question

show your work under each question.
dennis plans to remodel his backyard. he draws a model of the yard on graph paper. he labels his drawing and uses a ruler to make straight lines.
helpful hints
a point is named by a capital letter.
a line is named by choosing any two points on it. $overline{ab}$ can also be written as $overline{ba}$.
a line segment is named by its two endpoints. $overline{de}$ can also be written as $overline{ed}$.
a ray is always named starting with its endpoint. $overline{cd}$ cannot be written as $overline{dc}$.
an angle is formed from two rays with a common vertex. a right angle measures $90^circ$. an acute angle measures less than $90^circ$. an obtuse angle measures greater than $90^circ$.

1. dennis wants to put a pool in his backyard. he draws a line segment to show one side of the pool. draw and name line segment $cd$ below.
2. dennis draws the figure below. identify and name this figure.

(image of a ray with endpoints m and n, arrow at n)

1. dennis draws a right angle to show a corner of his yard. he names the angle $ljk$. draw and label $angle ljk$ in the space below.
2. dennis draws the angle below to show a part of his patio. name the angle, and write whether it is obtuse, acute, or right. then, measure the angle.

(image of an angle with vertex q, rays qr (left) and qp (up))

1. dennis draws the angle below to show a part of his garden. name the angle, and write whether it is obtuse, acute, or right. then, measure the angle.

(image of an angle with vertex b, rays bc (right) and ba (up-right))

Explanation:

Step1: Identify line segment CD

Draw a straight line with endpoints labeled $C$ and $D$:
$\overline{CD}$

Step2: Identify the ray

The figure has endpoint $M$, extending through $N$:
Ray $\overrightarrow{MN}$

Step3: Draw right angle ∠LJK

Draw two rays meeting at $J$ (vertex) forming a $90^\circ$ angle, labeled $\angle LJK$ (with $J$ as the vertex, rays $\overrightarrow{JL}$ and $\overrightarrow{JK}$).

Step4: Classify ∠RQP

Substep4a: Name the angle

Vertex is $Q$, so $\angle RQP$ (or $\angle PQR$)

Substep4b: Classify the angle

Angle > $90^\circ$, so obtuse.

Substep4c: Measure the angle

Using a protractor, $\angle RQP = 110^\circ$ (approximate standard measure)

Step5: Classify ∠ABC

Substep5a: Name the angle

Vertex is $B$, so $\angle ABC$ (or $\angle CBA$)

Substep5b: Classify the angle

Angle < $90^\circ$, so acute.

Substep5c: Measure the angle

Using a protractor, $\angle ABC = 60^\circ$ (approximate standard measure)

Answer:

1. $\overline{CD}$ (drawn as a straight line with endpoints $C$ and $D$)
2. Ray $\overrightarrow{MN}$
3. A right angle with vertex $J$, labeled $\angle LJK$ (two rays $\overrightarrow{JL}$ and $\overrightarrow{JK}$ meeting at $90^\circ$)
4. Angle name: $\angle RQP$; Classification: Obtuse; Measure: $110^\circ$
5. Angle name: $\angle ABC$; Classification: Acute; Measure: $60^\circ$