Question

precisely defining mathematical terms
angle and circle
how can we define the mathematical terms angle and circle?
angle
∠______
∠ bac
∠______
an angle is formed by two rays with a
common ______
circle
draw circle y. label ra... length r.
a circle is defined as all... plane equidistant from a...

Explanation:

Step1: Identify the angle notation

The angle at vertex \( A \) with rays \( AB \) and \( AC \) can be denoted as \( \angle CAB \) (or \( \angle BAC \) which is already given, and also \( \angle 1 \) as labeled). For the first blank, since it's the angle at \( A \) with the two rays, we can use \( \angle CAB \) or \( \angle 1 \). For the second blank, using the vertex and the two points, another notation is \( \angle BAC \) (already given) or \( \angle 1 \), but also \( \angle CAB \) or \( \angle BAC \) variants. Wait, looking at the diagram, the angle is \( \angle BAC \) (or \( \angle CAB \)) and also labeled as \( \angle 1 \). So the first blank (top) could be \( \angle CAB \) or \( \angle 1 \), the second blank (bottom) could be \( \angle 1 \) or \( \angle CAB \). Also, the definition of an angle: an angle is formed by two rays with a common endpoint (as filled in, which is correct because the two rays \( AB \) and \( AC \) meet at endpoint \( A \)).

Step2: Confirm angle notation

In angle notation, \( \angle BAC \) has vertex \( A \), with sides \( AB \) and \( AC \). So the first blank (above \( \angle BAC \)) can be \( \angle CAB \) (since order of the points can be reversed as long as the vertex is in the middle) or \( \angle 1 \) (the labeled angle). The second blank (below \( \angle BAC \)) can be \( \angle 1 \) or \( \angle CAB \). The definition part: "An angle is formed by two rays with a common endpoint" is correct because the two rays share the same endpoint (vertex \( A \)).

Answer:

For the angle notation blanks:

• First blank (top): \( \boldsymbol{\angle CAB} \) (or \( \boldsymbol{\angle 1} \))
• Second blank (bottom): \( \boldsymbol{\angle 1} \) (or \( \boldsymbol{\angle CAB} \))

For the definition: "An angle is formed by two rays with a common \(\boldsymbol{\text{endpoint}}\)" (which is already filled correctly in the image).

(If the question is about filling the blanks for angle notation: the first blank can be \( \angle CAB \) or \( \angle 1 \), the second blank can be \( \angle 1 \) or \( \angle CAB \); the definition blank is "endpoint".)