Basic geometric concepts and notations

{"questions":[{"content":"How many straight lines can pass through two distinct points?[[choice-1]]","widgets":{"choice-1":{"type":"choice","options":["Exactly one","Two","Three","Infinitely many"],"answer":[0]}},"hints":["Recall the axiom about a straight line through two distinct points.","Exactly one straight line passes through any two distinct points."]},{"content":"Which angle is a right angle?[[choice-11]]","widgets":{"choice-11":{"type":"choice","options":["An angle measuring $45^\\circ$","An angle measuring $90^\\circ$","An angle measuring $0^\\circ$","An angle measuring $180^\\circ$"],"answer":[1]}},"hints":["Recall the definition of a right angle.","A right angle measures $90^\\circ$."]},{"content":"Which points do not lie on the line?[[choice-29]][[image-46]]","widgets":{"choice-29":{"type":"choice","options":["$A$ and $B$","$C$ and $D$","$A$ and $C$","$D$ and $B$"],"answer":[1]},"image-46":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2026/01/1-01-14.svg","width":"300"}},"hints":["A point that is not on the line does not belong to it."]},{"content":"How many straight lines can pass through one point?[[choice-70]]","widgets":{"choice-70":{"type":"choice","options":["Exactly one","Two","Infinitely many","None"],"answer":[2]}},"hints":["A line through a given point can have any direction.","Infinitely many lines can pass through one point in different directions."]},{"content":"Which lines are parallel?[[choice-111]]","widgets":{"choice-111":{"type":"choice","options":["Lines that intersect.","Lines that share a point.","Lines in the same plane that do not intersect.","Lines that intersect at an angle of $90^\\circ$."],"answer":[2]}},"hints":["These lines have no points in common.","Parallel lines do not intersect."]},{"content":"Which angle is an acute angle?[[choice-167]]","widgets":{"choice-167":{"type":"choice","options":["An angle greater than $90^\\circ$.","An angle measuring $90^\\circ$.","An angle less than $90^\\circ$.","An angle measuring $180^\\circ$."],"answer":[2]}},"hints":["Recall the definition of an acute angle.","An acute angle is smaller than a right angle."]},{"content":"What is a line segment?[[choice-230]]","widgets":{"choice-230":{"type":"choice","options":["A part of a line with no endpoints.","A part of a line with a starting point.","A part of a line bounded by two endpoints.","A closed curve."],"answer":[2]}},"hints":["A line segment has two endpoints.","It lies on a straight line and is bounded by two endpoints."]},{"content":"Which lines are perpendicular?[[choice-304]]","widgets":{"choice-304":{"type":"choice","options":["Lines that intersect at an angle of $90^\\circ$.","Intersecting lines.","Lines that do not intersect.","Lines that intersect at an angle of $60^\\circ$."],"answer":[0]}},"hints":["Perpendicular lines form a right angle.","A right angle measures $90^\\circ$."]},{"content":"Which of these geometric objects has a starting point but extends endlessly in one direction?[[choice-390]]","widgets":{"choice-390":{"type":"choice","options":["Line segment","Straight line","Ray","Circle"],"answer":[2]}},"hints":["This object is part of a straight line and extends endlessly in one direction.","This object is called a ray."]},{"content":"How many points can parallel lines have in common?[[choice-486]]","widgets":{"choice-486":{"type":"choice","options":["Infinitely many","One","Two","None"],"answer":[3]}},"hints":["Parallel lines do not intersect.","If two distinct lines have a point in common, they are not parallel."]},{"content":"Which points lie on the line?[[choice-592]][[image-111]]","widgets":{"choice-592":{"type":"choice","options":["$A$ and $B$","$C$ and $B$","$C$ and $D$","$A$ and $D$"],"answer":[0]},"image-111":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2026/01/1-01-14.svg","width":"300"}},"hints":["A point that lies on the line belongs to it."]},{"content":"What is a ray?[[choice-710]]","widgets":{"choice-710":{"type":"choice","options":["A straight line with no endpoints.","A straight line bounded at both ends.","A part of a line with one endpoint that extends endlessly in one direction.","A broken line."],"answer":[2]}},"hints":["A ray has exactly one endpoint."]},{"content":"Which lines are intersecting lines?[[choice-827]]","widgets":{"choice-827":{"type":"choice","options":["Lines that coincide.","Lines with no points in common.","Lines with exactly one point in common.","Lines lying in different planes."],"answer":[2]}},"hints":["These lines have one point of intersection."]},{"content":"Which is larger: an acute angle or an obtuse angle?[[choice-954]]","widgets":{"choice-954":{"type":"choice","options":["It cannot be determined","An acute angle","An obtuse angle","They are equal"],"answer":[2]}},"hints":["An acute angle is less than $90^\\circ$; an obtuse angle is greater."]},{"content":"Which angle is an obtuse angle?[[choice-1105]]","widgets":{"choice-1105":{"type":"choice","options":["An angle less than $90^\\circ$.","An angle measuring $90^\\circ$.","An angle greater than $90^\\circ$ but less than $180^\\circ$.","An angle measuring $180^\\circ$."],"answer":[2]}},"hints":["An acute angle is smaller than a right angle, which measures $90^\\circ$.","An obtuse angle is larger than a right angle."]}]}

{"questions":[{"content":"Point $A$ lies on line $m$. How is this written?[[choice-1]][[image-49]]","widgets":{"choice-1":{"type":"choice","options":["$A \\perp m$","$A \\in m$","$A \\parallel m$","$A \\subset m$"],"answer":[1]},"image-49":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2026/01/2-01-15.svg","width":"300"}},"hints":["If a point lies on a line, it belongs to that line.","The membership symbol is written as $ \\in$."]},{"content":"How many straight lines can pass through one point?[[choice-9]]","widgets":{"choice-9":{"type":"choice","options":["One","Two","None","Infinitely many"],"answer":[3]}},"hints":["Recall the basic property of a straight line through two points.","Exactly one straight line passes through two distinct points."]},{"content":"How many straight lines can pass through two distinct points?[[choice-20]]","widgets":{"choice-20":{"type":"choice","options":["One","Two","Four","Many"],"answer":[0]}},"hints":["Recall the geometric axiom about a straight line through two points.","Exactly one straight line passes through two distinct points."]},{"content":"Which lines are parallel?[[choice-52]]","widgets":{"choice-52":{"type":"choice","options":["Lines with exactly one point in common.","Lines that intersect at a right angle.","Lines in the same plane that do not intersect.","Lines of equal length."],"answer":[2]}},"hints":["Think of the two rails of a straight railway track.","Notice that the lines have no points in common."]},{"content":"Which angle is a right angle?[[choice-93]]","widgets":{"choice-93":{"type":"choice","options":["An angle measuring $45^\\circ$.","An angle measuring $90^\\circ$.","An angle measuring $180^\\circ$.","An angle measuring $120^\\circ$."],"answer":[1]}},"hints":["A right angle is formed where perpendicular lines intersect.","Perpendicular lines intersect at an angle of $90^\\circ$."]},{"content":"What is a ray?[[choice-155]]","widgets":{"choice-155":{"type":"choice","options":["A part of a straight line bounded at both ends.","A part of a straight line bounded at one end.","An unbounded straight line.","The distance between two points."],"answer":[1]}},"hints":["A ray has one endpoint and extends endlessly in one direction."]},{"content":"What is a line segment?[[choice-213]]","widgets":{"choice-213":{"type":"choice","options":["A part of a straight line bounded at one end.","A part of a straight line bounded at both ends.","A stroke.","A dashed line."],"answer":[1]}},"hints":["A line segment can be measured with a ruler.","A line segment has two endpoints."]},{"content":"If point $B$ does not lie on line $a$, how is this written?[[choice-302]][[image-118]]","widgets":{"choice-302":{"type":"choice","options":["$B \\in a$","$B \\subset a$","$B \\notin a$","$B \\perp a$"],"answer":[2]},"image-118":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2026/01/3-01-14.svg","width":"300"}},"hints":["Recall the membership symbol.","If a point does not belong to a line, the membership symbol is crossed out."]},{"content":"Which lines share one point and form an angle of $90^\\circ$?[[choice-373]]","widgets":{"choice-373":{"type":"choice","options":["Parallel","Intersecting","Perpendicular","Coincident"],"answer":[2]}},"hints":["These lines form a right angle and are called perpendicular lines."]},{"content":"Which statement is true?[[choice-450]]","widgets":{"choice-450":{"type":"choice","options":["Infinitely many straight lines pass through two distinct points.","Exactly one straight line passes through a single point.","Parallel lines intersect at a right angle.","Exactly one straight line passes through two distinct points."],"answer":[3]}},"hints":["Recall the basic property of a straight line through two points.","Exactly one straight line can be drawn through any two distinct points."]},{"content":"Which angle is an obtuse angle?[[choice-545]]","widgets":{"choice-545":{"type":"choice","options":["An angle less than $90^\\circ$.","An angle measuring $90^\\circ$.","An angle greater than $90^\\circ$ but less than $180^\\circ$.","An angle measuring $180^\\circ$."],"answer":[2]}},"hints":["An obtuse angle is always larger than an acute angle.","It is larger than a right angle but smaller than a straight angle."]},{"content":"How do you write, using a symbol, that line $a$ is perpendicular to line $b$?[[choice-704]][[image-191]]","widgets":{"choice-704":{"type":"choice","options":["$a \\parallel b$","$a \\perp b$","$a \\in b$","$a \\cap b$"],"answer":[1]},"image-191":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2026/01/4-01-13.svg","width":"300"}},"hints":["The perpendicular symbol looks like an upside-down capital T.","The correct notation is $a \\perp b$."]},{"content":"How do you write, using a symbol, that line $a$ is parallel to line $b$?[[choice-846]]","widgets":{"choice-846":{"type":"choice","options":["$a \\perp b$","$a \\cap b$","$a \\parallel b$","$a \\in b$"],"answer":[2]}},"hints":["Parallel lines do not intersect, and the parallel symbol reflects this.","The correct notation is $a \\parallel b$."]},{"content":"How do you write that line $a$ intersects line $b$?[[choice-999]][[image-434]]","widgets":{"choice-999":{"type":"choice","options":["$a \\parallel b$","$a \\perp b$","$a \\cap b$","$a \\in b$"],"answer":[2]},"image-434":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2026/01/5-01-8.svg","width":"300"}},"hints":["The intersection symbol resembles an upside-down horseshoe.","The correct notation is $a \\cap b$."]},{"content":"Which notation correctly names the angle shown?[[choice-1163]][[image-268]]","widgets":{"choice-1163":{"type":"choice","options":["$\\angle EDF$","$\\angle EFD$","$\\angle DFE$","$\\angle DEF$"],"answer":[3]},"image-268":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2026/01/4_2-01.svg","width":"300"}},"hints":["Notice which letter marks the vertex of the angle.","The letter marking the vertex must be in the middle."]},{"content":"Which notation correctly names the angle shown?[[choice-1324]][[image-349]]","widgets":{"choice-1324":{"type":"choice","options":["$\\angle CBA$","$\\angle BAC$","$\\angle CAB$","$\\angle BCA$"],"answer":[0]},"image-349":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2026/01/5_2-01.svg","width":"300"}},"hints":["Notice which letter marks the vertex of the angle.","The letter marking the vertex must be in the middle."]}]}