 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