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9-12 Geometry Unit 5 Lesson 2

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K-5 Math 6-8 Math •9-12 Math

Course

Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

Unit

Unit 1 Unit 2 Unit 3 Unit 4 •Unit 5 Unit 6 Unit 7 Unit 8

Lesson

Lesson 1 •Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
Lesson 18

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Unit 5, Lesson 2

Slicing Solids

Geometry

Practice

Problem 1

Imagine slicing each figure into parallel cross-sections. Select all figures that have congruent cross-sections in a particular direction.

triangular pyramid
square pyramid
rectangular prism
cube
cone
cylinder
sphere

Problem 2

Imagine an upright cone with its base resting on your horizontal desk.
Sketch the cross-section formed by intersecting each plane with the cone.

vertical plane not passing through the cone’s topmost point
horizontal plane
diagonal plane

Problem 3

Name 2 figures for which a circle can be a cross-section.

Problem 4

ForLesson 1: Solids of Rotation

Sketch the solid of rotation formed by rotating the given two-dimensional figure using the dashed vertical line as an axis of rotation.

<p>Dotted vertical line. Next to it is a wavy line, vaguely resembling the number 3.</p>

Problem 5

ForLesson 1: Solids of Rotation

Draw a two-dimensional figure that could be rotated using a vertical axis of rotation to give the cone shown.

<p>A cone with a dotted vertical line down its middle.</p>

Problem 6

ForLesson 12: Approximating Pi

A regular hexagon and a regular octagon are both inscribed in the same circle. Which of these statements is true?

The perimeter of the hexagon is less than the perimeter of the octagon, and each perimeter is less than the circumference of the circle.
The perimeter of the octagon is less than the perimeter of the hexagon, and each perimeter is less than the circumference of the circle.
The perimeter of the hexagon is greater than the perimeter of the octagon, and each perimeter is greater than the circumference of the circle.
The perimeter of the octagon is greater than the perimeter of the hexagon, and each perimeter is greater than the circumference of the circle.

Problem 7

ForLesson 11: Solving Problems with Trigonometry

Technology required. Find the perimeter of the figure.

<p>Quadrilateral ABCE. Angles B and C = 90 degrees. Angle E = 70 degrees. Side AB = 8, side BC=10.</p>

Problem 8

ForLesson 6: Working with Trigonometric Ratios

Match each trigonometric function to a ratio. You may use ratios more than once.

<p>Right triangle A B C. Angle A C B is 90 degrees, A C is x units, B C is y units, A B is z units.</p>

\(\tan(A)\)
\(\tan(B)\)
\(\cos(A)\)
\(\cos(B)\)
\(\sin(A)\)
\(\sin(B)\)

\(\frac{y}{z}\)
\(\frac{x}{z}\)
\(\frac{x}{y}\)
\(\frac{y}{x}\)

Problem 9

ForLesson 20: Transformations, Transversals, and Proof

Explain how you know that lines \(m\) and \(ℓ\) are parallel.

<p>Triangle A B C. A C on line L. Point D on A B, point E on B C. Line m runs through points D and E. Angles B A C and B D E congruent.</p> — \(\angle {BDE} \cong \angle {BAC}\)