Lines & Symmetry
Question: A shape can be folded along a line so that both halves match exactly.
What is this line called?
Answer: A line of symmetry
A line of symmetry divides a figure into two matching halves.
Question: An angle measures 35°.
Is it acute or obtuse?
Answer: Acute
An acute angle measures less than 90°.
Since:
35° < 90°
the angle is acute.
Question: What fraction of a full turn is a quarter turn?
Answer: 1/4
A full turn can be divided into 4 equal quarter turns.
Question: Two lines run next to each other and will never meet, even if they are extended forever.
What are these lines called?
Answer: Parallel lines
Parallel lines stay the same distance apart and never intersect.
Question: A student says:
“Every angle smaller than 180° is acute.”
Is the student correct?
Answer: No.
An acute angle is less than 90°.
An obtuse angle is greater than 90° but less than 180°.
So an angle such as 120° is less than 180° but is obtuse, not acute.
Question: Which shape has exactly 4 lines of symmetry?
A. A rectangle that is not a square
B. A square
C. A scalene triangle
D. A parallelogram
Answer: B. A square
A square has 4 lines of symmetry: 2 through the middle of opposite sides and 2 through opposite corners.
Question: An angle measures 125°.
Is it acute or obtuse?
Answer: Obtuse
An obtuse angle measures more than 90° but less than 180°.
Since:
90° < 125° < 180°
the angle is obtuse.
Question: How many degrees are in a half turn?
Answer: 180°
A full turn is 360°.
Half of 360° is:
360° ÷ 2 = 180°
Question: Two lines meet to form a 90° angle.
What are the lines called?
Answer: Perpendicular lines
Perpendicular lines intersect at a right angle.
Question: A student says:
“A half turn measures 90°.”
Is the student correct?
Answer: No.
A full turn is 360°.
A half turn is:
360° ÷ 2 = 180°
A quarter turn is 90°.
Question: A student says:
“A rectangle has 4 lines of symmetry because it has 4 sides.”
Is the student correct?
Answer: No.
A rectangle that is not a square has 2 lines of symmetry.
Its lines of symmetry go through the middle of the rectangle horizontally and vertically.
Question: Without using a protractor, which is the most reasonable estimate for an obtuse angle?
A. 25°
B. 72°
C. 118°
D. 180°
Answer: C. 118°
An obtuse angle is greater than 90° and less than 180°.
So 118° is a reasonable estimate.
Question: How many degrees are in a quarter turn?
Answer: 90°
A quarter turn is:
360° ÷ 4 = 90°
Question: A student says:
“The opposite sides of a rectangle are perpendicular.”
Is the student correct?
Answer: No.
The opposite sides of a rectangle are parallel.
The sides that meet at each corner are perpendicular because they form right angles.
Question: A student draws two lines that intersect at a right angle.
They say:
“These lines are parallel because they are both straight.”
Are they correct?
Answer: No.
The lines intersect, so they cannot be parallel.
Because they meet at a 90° angle, they are perpendicular.
Question: A shape has a vertical line of symmetry and a horizontal line of symmetry.
When the shape is reflected across either line, the two halves match.
How many lines of symmetry does the shape have at minimum?
Answer: 2 lines of symmetry
It has both a vertical and a horizontal line of symmetry.
Question: A straight angle measures 180°.
One part of the angle measures 65°.
What is the measure of the other part?
Answer: 115°
The two angles make a straight angle:
65° + ? = 180°
180° − 65° = 115°
So the missing angle is 115°.
Question: A robot turns three-fourths of a full turn.
How many degrees does the robot turn?
Answer: 270°
A full turn is 360°.
Three-fourths is:
360° ÷ 4 = 90°
90° × 3 = 270°
So the robot turns 270°.
Question: You are given a line segment labeled AB.
You need to draw another line through point C that is parallel to AB.
What should you look for to make sure your new line is correct?
Answer:
The new line should:
These are characteristics of parallel lines.
Question: A student measures an angle and gets 145°.
They say:
“This must be an acute angle because 145 is less than 180.”
Is the student correct?
Answer: No.
An acute angle is less than 90°.
Since:
90° < 145° < 180°
the angle is obtuse.
Question: Two students are discussing a figure.
The figure is a square.
Who is correct? Explain.
Answer: Noah is correct.
A square has 4 lines of symmetry:
So the square has 4 lines of symmetry.
Question: Two angles together form a straight angle.
One angle is 42° and the other angle is p.
What is the measure of p?
Answer: 138°
A straight angle measures 180°.
So:
p + 42° = 180°
p = 180° − 42°
p = 138°
Question: A dancer turns one-half turn and then makes another quarter turn in the same direction.
What is the total angle of the turn?
Answer: 270°
Half turn:
180°
Quarter turn:
90°
Total:
180° + 90° = 270°
So the dancer turns 270°, or three-fourths of a full turn.
Question: A road runs east to west.
A second road crosses it and runs north to south.
The two roads meet at a 90° angle.
How would you describe the relationship between the two roads?
Answer: They are perpendicular.
They intersect to form a right angle, which measures 90°.
Question: A student is given these clues about a mystery angle:
What is the angle?
Answer: 120°
A half turn is:
180°
One-third of a half turn:
180° ÷ 3 = 60°
The angle is 60° more than 60°:
60° + 60° = 120°
Check:
90° < 120° < 180°
So the angle is 120°, which is obtuse.