Congruence: Precise Geometric Definitions from Undefined Terms (CCSS.G-CO.1)
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Common Core High School Geometry › Congruence: Precise Geometric Definitions from Undefined Terms (CCSS.G-CO.1)
Points A, B, and C form a right angle at B with $\angle ABC=90^\circ$. A straight path extends from B through C and continues past C.
Which option represents a ray starting at B and passing through C?
$\overrightarrow{BC}$
$\overrightarrow{CB}$
$\overline{BC}$
$\overleftrightarrow{BC}$
Explanation
A ray starts at an endpoint and extends forever in one direction. $\overrightarrow{BC}$ starts at B and goes through C. $\overrightarrow{CB}$ would start at C, and $\overline{BC}$ is a finite segment, while $\overleftrightarrow{BC}$ is a full line.
Segments $AB$ and $BC$ intersect at point B such that $AB \perp BC$.
What is the measure of $\angle ABC$?
$180^\circ$
$90^\circ$
$45^\circ$
$0^\circ$
Explanation
Perpendicular segments meet to form a right angle by definition, so $m\angle ABC=90^\circ$. It is not $180^\circ$ (a straight angle).
Points A, B, and C lie on a straight line in that order with $AB=5$ and $BC=3$.
Which option names the line segment from A to B?
$\overleftrightarrow{AB}$
$\overrightarrow{AB}$
$\overline{AB}$
$\overline{BC}$
Explanation
A line segment is the part of a line between two endpoints; $\overline{AB}$ names the segment from A to B. $\overleftrightarrow{AB}$ is a full line through A and B, and $\overrightarrow{AB}$ is a ray starting at A. $\overline{BC}$ is a different segment.
In rectangle $ABCD$, $AB=6$ and $BC=4$.
Which segment is parallel to $\overline{AB}$?
$\overline{BC}$
$\overline{AD}$
$\overline{AC}$
$\overline{CD}$
Explanation
Opposite sides of a rectangle are parallel, so $\overline{AB} \parallel \overline{CD}$. $\overline{BC}$ and $\overline{AD}$ are perpendicular to $\overline{AB}$, and $\overline{AC}$ is a diagonal, not parallel to $\overline{AB}$.
A circle has center $O$. Point $A$ lies on the circle and $OA=5$.
Which option represents a radius of the circle?
$\overline{AB}$
$\overline{OA}$
$\overleftrightarrow{OA}$
$\overrightarrow{AO}$
Explanation
A radius is a segment from the center to a point on the circle, so $\overline{OA}$ is a radius. $\overline{AB}$ is a chord between two points on the circle, $\overleftrightarrow{OA}$ is a full line, and $\overrightarrow{AO}$ is a ray.