Math Unit 12

Study Guide

Unit 12: Geometry

Chapter 1- Examples of test questions:

Students may use an index card on the test for checking right angles – however, no writing should be on the card.
Understanding angles is an important part of Geometry.
- Right Angle (90 degrees – like the corner of a piece of paper)
- Acute Angle (smaller than a right angle)
- Obtuse Angle (wider than a right angle)
- Organize angles from smallest to largest or largest to smallest.
- Two lines that are not connected are not an angle.
- Polygons are closed figures with straight sides. Know the number of angles in polygons.
  - Triangle has three angles
  - Quadrilateral has four angles (with or without parallel sides)
    - Trapezoid has four angles (one pair of parallel sides)
    - Parallelogram has four angles (two pairs of parallel sides)
      - Rectangle has four (right) angles
      - Rhombus has four angles (four equal sides)
      - Square has four angles (four right angles and four equal sides)
  - Pentagon has five angles
  - Hexagon has six angles
  - Octagon has eight angles
- Which polygon has eight lines and eight angles? (octagon)
- Pick a specific polygon from a row of shapes.
  - Various shapes drawn. Which is the octagon?
  - Compare shapes. The hexagon has ___ more sides/angles than the triangle.
- Draw an angle larger or smaller than the one drawn.

Chapter 2- Examples of test questions:

Draw a right angle using the corner of a piece of paper.
Choose right angles from drawn angles.
Choose triangles that have right angle(s).
Choose angles that are greater/smaller than a right angle.
Array of dots are given. Create an angle within the array. There will be instructions on what type of angle to include (obtuse, right, acute).
Know how many angles are in various shapes. For example, how many right angles are there in a rectangle?
Name a shape with a specific description. For example, name a shape that has five angles.

Chapter 3- Examples of test questions:

Pick parallelograms from various shapes. Pick shapes that are not parallelograms from various shapes.
Pick specific shapes. For example, shapes are drawn and choose quadrilateral.
Compare shapes.
- Is a rectangle a rhombus?
- Is a hexagon a parallelogram?
- Which quadrilateral has unequal sides? Which quadrilateral doesn’t have right angles? Which quadrilateral has one right angle?
Triangles:
- An obtuse triangle has one angle greater than 90 degrees.
- A right triangle has an angle at 90 degrees.
- An acute triangle has three angles smaller than 90 degrees.
- A scalene triangle has all sides different in length.
- An isosceles triangle has two equal sides. Since an equilateral has three equal sides it is also “isosceles” since it has at least two equal sides!
- An equilateral triangle has three equal sides.
Questions regarding triangles. For example, what do you call a triangle that all sides have different lengths?
True or false statements comparing information on triangles.
- Can an isosceles triangle have a right angle?
- Can an equilateral triangle be scalene?
Various triangles drawn.
- Which triangles are scalene, isosceles, or equilateral?
- Which triangles are obtuse, right, or acute?

Chapter 4- Examples of test questions:

A polygon is a closed plane figure, with straight sides.
- Rectangles, squares, and triangles
A regular polygon is a polygon in which the sides are all the same length and are symmetrically placed about a common center. It is both equiangular and equilateral.
- Square
A polyhedron is a three-dimensional solid consisting of a collection of polygons, joined at their edges.
- A general prism possesses two congruent polygonal faces and with all remaining faces parallelograms.
  - A right prism has the top and bottom polygons lying on top of each other so that the vertical polygons connecting their sides are not only parallelograms, but also rectangles.
- A pyramid is a polyhedron where one face is a polygon and all the other faces are triangles meeting at a common polygon vertex.
  - A right pyramid has the line joining the centroid of the base and the apex is perpendicular to the base.
  - A regular pyramid is a right pyramid whose base is a regular polygon.
- All prisms and pyramids in this unit will be right prisms or pyramids.
- A cylinder is a solid bounded by two congruent circular bases, one directly above the other.
The flat surface of a solid is its face.
- How many faces does a shoebox have? (six)
- How many faces does a sphere have? (none)
- How many faces does a cylinder have? (two)
- How many faces does a triangular pyramid have? (four)
- How many faces does a rectangular pyramid have? (five)
- How many faces does a cone have? (one)
An edge is where two faces meet.
- How many edges does a shoebox have? (twelve)
- How many edges does a sphere have? (none)
- How many edges does a cylinder have? (two)
- How many edges does a triangular pyramid have? (six)
- How many edges does a rectangular pyramid have? (eight)
- How many edges does a cone have? (none)
A vertex is the point where two or more edges meet.
- How many vertices does a shoebox have? (eight)
- How many vertices does a sphere have? (none)
- How many vertices does a cylinder have? (none)
- How many vertices does a triangular pyramid have? (four)
- How many vertices does a rectangular pyramid have? (five)
- How many vertices does a cone have? (one)
Solids will be drawn.
- Name the solid drawn.
- Find a specific solid. For example, mark the rectangular pyramid.
- Describe the solid.
  - How many faces does a cone have?
  - How many edges does a triangular pyramid have?
  - How many vertices does a sphere have?
Various shapes will be drawn together. List the shapes that make up the figure.
Fill in a table asking for the number of faces, edges, and vertices of various solids.

Unit 12 Cumulative Test:

Review all of Units 1 - 12