3B · Chapter 12 · review
Chapter review
Original cumulative chapter practice to consolidate taught ideas.
Original cumulative chapter practice to consolidate taught ideas. Solutions are available as revealable feedback and in a separate complete answer key. No answer submissions or accounts are required.
Assessment · 26 questions
Questions
Show your thinking; use diagrams when they help. Do not open solutions during your first attempt.
- A1
A circle has radius 29 cm. What is its diameter?
Reveal explanation
Answer: 58 cm
A diameter joins two radii end to end through the center: 29 + 29 = 58 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - A2
An angle measures 170°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 170° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 170 degrees; angle size depends on rotation, not ray length. - A3
An angle measures 29°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 29° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 29 degrees; angle size depends on rotation, not ray length. - A4
A triangle has side lengths 5, 6, and 7 units. Classify it by its side lengths.
Reveal explanation
Answer: scalene
Scalene means no equal sides. These lengths satisfy the triangle inequality.
- A5
A triangle has side lengths 9, 9, and 9 units. Classify it by its side lengths.
Reveal explanation
Answer: equilateral
Equilateral means three equal sides. These lengths satisfy the triangle inequality.
- A6
Identify the most specific shape: a quadrilateral has four right angles and four equal sides of 11 cm.
Reveal explanation
Answer: square
The shape is a square. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.
- A7
Using a compass set to 13 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 13 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 13 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - A8
A circle has radius 15 cm. What is its diameter?
Reveal explanation
Answer: 30 cm
A diameter joins two radii end to end through the center: 15 + 15 = 30 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - A9
An angle measures 119°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 119° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 119 degrees; angle size depends on rotation, not ray length. - A10
An angle measures 113°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 113° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 113 degrees; angle size depends on rotation, not ray length. - A11
A triangle has side lengths 4, 4, and 4 units. Classify it by its side lengths.
Reveal explanation
Answer: equilateral
Equilateral means three equal sides. These lengths satisfy the triangle inequality.
- A12
A triangle has side lengths 3, 3, and 3 units. Classify it by its side lengths.
Reveal explanation
Answer: equilateral
Equilateral means three equal sides. These lengths satisfy the triangle inequality.
- A13
Identify the most specific shape: a quadrilateral has two pairs of parallel sides, side lengths 9 and 11 cm, and no right angles.
Reveal explanation
Answer: parallelogram
The shape is a parallelogram. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.
- A14
Using a compass set to 20 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 20 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 20 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - A15
A circle has diameter 30 cm. What is its radius?
Reveal explanation
Answer: 15 cm
The radius is half the diameter. 30 ÷ 2 = 15 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - A16
An angle measures 39°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 39° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 39 degrees; angle size depends on rotation, not ray length. - A17
An angle measures 136°. Is it acute, right, or obtuse?
Reveal explanation
Answer: obtuse
Compare 136° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 136 degrees; angle size depends on rotation, not ray length. - A18
A triangle has side lengths 7, 7, and 7 units. Classify it by its side lengths.
Reveal explanation
Answer: equilateral
Equilateral means three equal sides. These lengths satisfy the triangle inequality.
- A19
A triangle has side lengths 6, 7, and 8 units. Classify it by its side lengths.
Reveal explanation
Answer: scalene
Scalene means no equal sides. These lengths satisfy the triangle inequality.
- A20
Identify the most specific shape: a quadrilateral has four right angles, adjacent side lengths 3 cm and 5 cm.
Reveal explanation
Answer: rectangle
The shape is a rectangle. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.
- A21
Using a compass set to 2 cm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 2 cm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 2 cm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - A22
A circle has radius 20 cm. What is its diameter?
Reveal explanation
Answer: 40 cm
A diameter joins two radii end to end through the center: 20 + 20 = 40 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - A23
An angle measures 59°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 59° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 59 degrees; angle size depends on rotation, not ray length. - A24
An angle measures 32°. Is it acute, right, or obtuse?
Reveal explanation
Answer: acute
Compare 32° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.
Angle of 32 degrees; angle size depends on rotation, not ray length. - A25
An angle is 65°. A student calls it obtuse because the rays look long. Explain the error.
Reveal explanation
Answer: Acute
65° is below 90°, so the angle is acute; ray length is irrelevant.
- A26
Two circles have diameters 8 cm and 10 cm. Which has the larger radius and by how much?
Reveal explanation
Answer: Second circle, by 1 cm
Their radii are 4 cm and 5 cm; changing diameter by 2 cm changes radius by 1 cm.