Chapter 16: worked solutions and marking guide
38 review answers and 38 exam answers
Chapter review solutions
Two lines meet at a 80° angle. Are they perpendicular? Explain.
Only a 90° intersection is perpendicular.
Two drawn straight lines have perpendicular separation 6 cm at one location and 6 cm at another. Does this observation support the claim that their separation is constant?
Parallel lines must keep a constant perpendicular separation.
Draw a horizontal line at row 6 and explain whether it is perpendicular to the vertical red reference.
Vertical and horizontal grid lines form 90° angles.
Can a rectangle be a parallelogram? Justify.
Both opposite side pairs of the named shape are parallel.
A pattern on a card has the shape of a square. How many reflection-symmetry lines does it have?
Square figures have 4 exact fold axes.
Reflect vertices (1,1), (5,3), and (3,5) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Two lines meet at a 155° angle. Are they perpendicular? Explain.
Only a 90° intersection is perpendicular.
Two drawn straight lines have perpendicular separation 4 cm at one location and 4 cm at another. Does this observation support the claim that their separation is constant?
Parallel lines must keep a constant perpendicular separation.
Using the vertical reference line on the grid, draw a perpendicular through grid row 5 and another distinct parallel vertical line at least 2 grid spaces away. Label both.
The horizontal makes 90° with the reference and the vertical has equal direction.
A rectangle has a side measuring 3 cm. State two defining angle or side properties of that type of quadrilateral.
The class-specific properties do not depend on the scale of a drawing.
A pattern on a card has the shape of a scalene triangle. How many reflection-symmetry lines does it have?
Scalene triangle figures have 0 exact fold axes.
Reflect vertices (2,1), (5,2), and (3,5) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Two lines meet at a 140° angle. Are they perpendicular? Explain.
Only a 90° intersection is perpendicular.
Two drawn straight lines have perpendicular separation 1 cm at one location and 1 cm at another. Does this observation support the claim that their separation is constant?
Parallel lines must keep a constant perpendicular separation.
Using the vertical reference line on the grid, draw a perpendicular through grid row 6 and another distinct parallel vertical line at least 1 grid spaces away. Label both.
The horizontal makes 90° with the reference and the vertical has equal direction.
State two defining geometric properties of a parallelogram.
Use side lengths, parallelism, and right angles—not appearance.
A folded shape has the shape of an equilateral triangle. How many reflection-symmetry lines does it have?
Equilateral triangle figures have 3 exact fold axes.
Reflect vertices (1,1), (4,2), and (2,6) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
An angle beside another makes 180°. If the first angle is 70°, find the neighbor and decide if the lines are perpendicular.
Adjacent angles total 180°. Both are right angles only when the first is 90°.
Two drawn straight lines have perpendicular separation 8 cm at one location and 8 cm at another. Does this observation support the claim that their separation is constant?
Parallel lines must keep a constant perpendicular separation.
Draw a horizontal line at row 5 and explain whether it is perpendicular to the vertical red reference.
Vertical and horizontal grid lines form 90° angles.
State two defining geometric properties of a square.
Use side lengths, parallelism, and right angles—not appearance.
A paper cutout has the shape of a scalene triangle. How many reflection-symmetry lines does it have?
Scalene triangle figures have 0 exact fold axes.
Reflect vertices (2,2), (4,2), and (2,6) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Two lines meet at a 135° angle. Are they perpendicular? Explain.
Only a 90° intersection is perpendicular.
Two drawn straight lines have perpendicular separation 5 cm at one location and 5 cm at another. Does this observation support the claim that their separation is constant?
Parallel lines must keep a constant perpendicular separation.
Construct a rectangle 6 grid spaces wide and 5 grid spaces high using parallel and perpendicular edges.
Opposite sides are parallel and adjacent sides meet at 90°.
A square has a side measuring 14 cm. State two defining angle or side properties of that type of quadrilateral.
The class-specific properties do not depend on the scale of a drawing.
A pattern on a card has the shape of a circle. How many reflection-symmetry lines does it have?
Circle figures have infinitely many exact fold axes.
Reflect vertices (2,2), (4,2), and (3,5) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
An angle beside another makes 180°. If the first angle is 110°, find the neighbor and decide if the lines are perpendicular.
Adjacent angles total 180°. Both are right angles only when the first is 90°.
Two drawn straight lines have perpendicular separation 4 cm at one location and 8 cm at another. Does this observation support the claim that their separation is constant?
Parallel lines must keep a constant perpendicular separation.
Two lines meet at a 145° angle. Are they perpendicular? Explain. Explain or sketch the mathematical relationship.
Only a 90° intersection is perpendicular. State which quantities or geometric properties justify the method.
Two drawn straight lines have perpendicular separation 5 cm at one location and 6 cm at another. Does this observation support the claim that their separation is constant? Explain or sketch the mathematical relationship.
Parallel lines must keep a constant perpendicular separation. State which quantities or geometric properties justify the method.
Construct a new vertical line 4 grid spaces right of the red vertical line. What is their relationship?
Both lines have the same vertical direction and stay a fixed distance apart.
Can a rectangle be a parallelogram? Justify. Explain or sketch the mathematical relationship.
Both opposite side pairs of the named shape are parallel. State which quantities or geometric properties justify the method.
A paper cutout has the shape of a non-square rectangle. How many reflection-symmetry lines does it have? Explain or sketch the mathematical relationship.
Non-square rectangle figures have 2 exact fold axes. State which quantities or geometric properties justify the method.
Reflect vertices (2,1), (5,3), and (3,5) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Practice examination solutions
A parallelogram has a side measuring 13 cm. State two defining angle or side properties of that type of quadrilateral.
The class-specific properties do not depend on the scale of a drawing.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Two drawn straight lines have perpendicular separation 3 cm at one location and 5 cm at another. Does this observation support the claim that their separation is constant?
Parallel lines must keep a constant perpendicular separation.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A chalkboard diagram has the shape of a square. How many reflection-symmetry lines does it have? Explain or sketch the mathematical relationship.
Square figures have 4 exact fold axes. State which quantities or geometric properties justify the method.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Two lines meet at a 25° angle. Are they perpendicular? Explain.
Only a 90° intersection is perpendicular.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A tile design has the shape of a circle. How many reflection-symmetry lines does it have?
Circle figures have infinitely many exact fold axes.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rhombus has a side measuring 13 cm. State two defining angle or side properties of that type of quadrilateral.
The class-specific properties do not depend on the scale of a drawing.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A parallelogram has a side measuring 6 cm. State two defining angle or side properties of that type of quadrilateral. Explain or sketch the mathematical relationship.
The class-specific properties do not depend on the scale of a drawing. State which quantities or geometric properties justify the method.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Two drawn straight lines have perpendicular separation 6 cm at one location and 8 cm at another. Does this observation support the claim that their separation is constant?
Parallel lines must keep a constant perpendicular separation.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Reflect vertices (1,1), (5,3), and (2,5) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
A chalkboard diagram has the shape of a circle. How many reflection-symmetry lines does it have?
Circle figures have infinitely many exact fold axes.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Reflect vertices (1,1), (4,3), and (2,7) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
A chalkboard diagram has the shape of an isosceles non-equilateral triangle. How many reflection-symmetry lines does it have?
Isosceles non-equilateral triangle figures have 1 exact fold axes.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Two lines meet at a 125° angle. Are they perpendicular? Explain.
Only a 90° intersection is perpendicular.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A folded shape has the shape of a non-square rectangle. How many reflection-symmetry lines does it have?
Non-square rectangle figures have 2 exact fold axes.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Draw a horizontal line at row 2 and explain whether it is perpendicular to the vertical red reference.
Vertical and horizontal grid lines form 90° angles.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
Can a square be a parallelogram? Justify.
Both opposite side pairs of the named shape are parallel.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Reflect vertices (2,2), (4,3), and (2,7) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
Two lines meet at a 35° angle. Are they perpendicular? Explain.
Only a 90° intersection is perpendicular.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Two drawn straight lines have perpendicular separation 2 cm at one location and 3 cm at another. Does this observation support the claim that their separation is constant? Explain or sketch the mathematical relationship.
Parallel lines must keep a constant perpendicular separation. State which quantities or geometric properties justify the method.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Two lines meet at a 115° angle. Are they perpendicular? Explain.
Only a 90° intersection is perpendicular.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Draw a horizontal line at row 7 and explain whether it is perpendicular to the vertical red reference.
Vertical and horizontal grid lines form 90° angles.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
Two drawn straight lines have perpendicular separation 4 cm at one location and 5 cm at another. Does this observation support the claim that their separation is constant?
Parallel lines must keep a constant perpendicular separation.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A rectangle has a side measuring 11 cm. State two defining angle or side properties of that type of quadrilateral.
The class-specific properties do not depend on the scale of a drawing.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Two drawn straight lines have perpendicular separation 3 cm at one location and 4 cm at another. Does this observation support the claim that their separation is constant?
Parallel lines must keep a constant perpendicular separation.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Using the vertical reference line on the grid, draw a perpendicular through grid row 4 and another distinct parallel vertical line at least 4 grid spaces away. Label both.
The horizontal makes 90° with the reference and the vertical has equal direction.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
Reflect vertices (1,2), (4,2), and (4,5) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
Two lines meet at a 60° angle. Are they perpendicular? Explain. Explain or sketch the mathematical relationship.
Only a 90° intersection is perpendicular. State which quantities or geometric properties justify the method.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Draw a line parallel to the red reference 1 grid spaces to its left, then a perpendicular at row 2.
Parallel means equal direction; perpendicular means a 90° intersection.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Two lines meet at a 60° angle. Are they perpendicular? Explain.
Only a 90° intersection is perpendicular.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
A paper cutout has the shape of a circle. How many reflection-symmetry lines does it have?
Circle figures have infinitely many exact fold axes.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A tile design has the shape of an equilateral triangle. How many reflection-symmetry lines does it have?
Equilateral triangle figures have 3 exact fold axes.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Two drawn straight lines have perpendicular separation 2 cm at one location and 3 cm at another. Does this observation support the claim that their separation is constant?
Parallel lines must keep a constant perpendicular separation.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Two lines meet at a 55° angle. Are they perpendicular? Explain.
Only a 90° intersection is perpendicular.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Using the vertical reference line on the grid, draw a perpendicular through grid row 5 and another distinct parallel vertical line at least 1 grid spaces away. Label both.
The horizontal makes 90° with the reference and the vertical has equal direction.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
A rhombus has a side measuring 4 cm. State two defining angle or side properties of that type of quadrilateral.
The class-specific properties do not depend on the scale of a drawing.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Reflect vertices (2,2), (5,3), and (3,6) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
Must every parallelogram be a rectangle? Justify.
A rectangle has four right angles, but a general parallelogram does not have to.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.
Two drawn straight lines have perpendicular separation 9 cm at one location and 9 cm at another. Does this observation support the claim that their separation is constant?
Parallel lines must keep a constant perpendicular separation.
Scoring (3 points): 1 point for identifying the relationship; 1 point for the correct working or figure; 1 point for a justified answer.