115 practice questions covering Lines and Angles, organised into 1 topics.
115 questions include a written explanation.
Pick a topic below, or try the samples first.
To draw an angle of $60^\circ$, what is the first step?
ADraw a circle of any radius
BDraw two rays at random and then measure
CDraw a ray to act as one arm of the angle
DMark a dot at $60$ on the protractor first
Show answer and explanation
Correct answer: C - Draw a ray to act as one arm of the angle
You begin by drawing one arm, then place the protractor with its centre on that arm's endpoint and its baseline along the arm. Marking the scale before there is an arm to line up gives nothing to measure from, drawing rays at random will not produce the required angle, and no circle is needed.
Q2
medium
Is $\overrightarrow{PQ}$ the same as $\overrightarrow{QP}$?
ANo, they start at different endpoints and go in opposite directions
BYes, both name the same ray
CNo, because $\overrightarrow{QP}$ is not a ray
DYes, because both contain the points $P$ and $Q$
Show answer and explanation
Correct answer: A - No, they start at different endpoints and go in opposite directions
In naming a ray the first letter is the endpoint, so $\overrightarrow{PQ}$ starts at $P$ and $\overrightarrow{QP}$ starts at $Q$, giving two different rays pointing opposite ways. Containing the same two labelled points is not enough to make them equal, and $\overrightarrow{QP}$ is a perfectly valid ray.
Q3
medium
Why does a protractor carry two sets of numbers along its curved edge?
ASo an angle can be measured from either the left or the right baseline
BSo acute and obtuse angles need different protractors
CSo the protractor can measure reflex angles directly
DSo that lengths and angles can both be read
Show answer and explanation
Correct answer: A - So an angle can be measured from either the left or the right baseline
The two scales run in opposite directions so that whichever arm you line up with the baseline, you can still read the angle. A protractor does not measure lengths, the same instrument handles both acute and obtuse angles, and reflex angles must be worked out by subtraction rather than read directly.
Q4
easy
Two angles are drawn on tracing paper. How can you check which is larger by superposition?
ACount the letters used to name each angle
BPlace one on the other so the vertices and one arm coincide, then see which second arm is further round
CCompare the lengths of their arms
DCompare how much paper each drawing uses
Show answer and explanation
Correct answer: B - Place one on the other so the vertices and one arm coincide, then see which second arm is further round
Superposition means laying one angle on the other with vertices together and one arm matched; the angle whose remaining arm falls outside is the larger. Arm length, paper used and the naming letters tell you nothing about the amount of turn.
Q5
hard
A folding table has legs that make an angle with the tabletop. When the legs are folded flat against the underside of the top, what is that angle closest to?
A$180^\circ$
B$0^\circ$
C$45^\circ$
D$90^\circ$
Show answer and explanation
Correct answer: B - $0^\circ$
Folded flat, the legs lie along the underside of the top, so the two arms almost coincide and the angle is close to $0^\circ$. A fully opened leg stands at about $90^\circ$, $180^\circ$ would mean the legs point straight out in the opposite direction from the top, and $45^\circ$ is a half-open position.
Q6
medium
Three distinct points $A$, $B$ and $C$ lie on one straight line. How many different line segments do they determine?
A$2$
B$3$
C$4$
D$6$
Show answer and explanation
Correct answer: B - $3$
Each pair of points gives one segment, and three points form the pairs $AB$, $BC$ and $AC$, so $3$ segments. Answering $2$ forgets the segment joining the outer two points, and $6$ counts each segment twice by treating $\overline{AB}$ and $\overline{BA}$ as different.
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