# Section 7.7: Review for Chapter 7

Studying for a chapter examination is a personal process, one which nobody else can do for you. Simply take the time to review what you have done.

Here are the new terms in Chapter 7.

Acute angle [7.2]
Acute triangle [7.3]
Alternate exterior angles [7.2]
Alternate interior angles [7.2]
Angle [7.2]
Angle of depression [7.5]
Angle of elevation [7.5]
Axiom [7.1]
Base angles [7.3]
Base of a triangle [7.3]
Bolyai-Lobachevski geometry [7.6]
Compass [7.1]
Complementary angles [7.2]
Congruent [7.1]
Congruent angles [7.2]
Congruent triangles [7.3]
Construct [7.1]
Corresponding angles [7.2, 7.4]
Corresponding parts [7.3]
Corresponding sides [7.4]
Cosine [7.5]
Degree [7.2]
Divine proportion [7.6]
Elliptic geometry [7.6]
Equal angles [7.2]
Equilateral triangle [7.3]
Euclidean geometry [7.1]
Euclid’s postulates [7.1]
Exterior angle [7.3]
Golden ratio [7.6]
Golden rectangle [7.6]
Great circle [7.6]
Half-line [7.1]
Horizontal line [7.2]
Hyperbolic geometry [7.6]
Hypotenuse [7.4]
Inverse tangent [7.5]
Inverse trigonometric ratios [7.5]
Isosceles triangle [7.3]
Isosceles triangle property [7.3]
Legs of a triangle [7.5]
Line [7.1]
Line segment [7.1]
Line of symmetry [7.1]
Lobachevskian postulate [7.6]
Non-Euclidean geometries [7.1, 7.6]
Obtuse angle [7.2]
Obtuse triangle [7.3]
Opposite side [7.2]
Parallel lines [7.3]
Parallelogram [7.2]
Perpendicular lines [7.2]
Plane [7.1]
Point [7.1]
Polygon [7.2]
Postulate [7.1]
Projective geometry [7.6]
Protractor [7.2]
Pseudosphere [7.6]
Pythagorean theorem [7.5]
Ray [7.1]
Rectangle [7.2]
Reflection [7.1]
Regular polygon [7.2]
Rhombus [7.2]
Right angle [7.2]
Right triangle [7.3]
Scalene triangle [7.3]
Similar figures [7.1]
Similar triangle theorem [7.4]
Similar triangles [7.4]
Similarity [7.1]
Sine [7.5]
Square [7.2]
Straight angle [7.2]
Straightedge [7.1]
Sum of the measures of angles in any triangle [7.3]
Supplementary angles [7.2]
Surface [7.1]
Symmetry (line) [7.1]
Tangent [7.5]
Theorem [7.1]
Transformation [7.1]
Transformational geometry [7.1]
Transversal [7.2]
Trapezoid [7.2]
Triangle [7.2, 7.3]
Trigonometric ratios [7.5]
Undefined terms [7.1]
Vertex (pl vertices) [7.2]
Vertex angle [7.3]
Vertical angles [7.2]
Vertical line [7.2]
If you can describe the term, read on to the next one; if you cannot,
then look it up in the text (the section number is shown in brackets).

IMPORTANT IDEAS

Can you explain each of these important ideas in your own words?

Euclidean postulates [7.1]
Terminology associated with polygons, angles, and parallel/perpendicular lines [7.2]
Sum of the measures of angles in a triangle [7.3]
Exterior angles of a triangle [7.3]
Isosceles triangle property [7.3]
Similar triangle theorem [7.4]
Pythagorean theorem [7.5]
Golden rectangle and golden ratio [7.6]
Lobachevskian postulate [7.6]
Comparison of major two-dimensional geometries [7.6]

Next, make sure you understand the types of problems in Chapter 7.

TYPES OF PROBLEMS

Construct line segments. [7.1]
Construct circles, given the radius. [7.1]
Construct parallel lines. [7.1]
Find a line of symmetry for a given piece of art. [7.1]
Decide whether a given picture is symmetric. [7.1]
Visualize objects in three dimensions. [7.1]
Classify polygons with three to twelve sides. [7.2]
Construct an angle congruent to a given angle. [7.2]
Classify angles. [7.2]
Identify vertical, horizontal, intersecting, and parallel lines. [7.2]
Name the corresponding parts of congruent triangles. [7.3]
Find the measure of the third angle of a triangle. [7.3]
Find the measure of the exterior angles of a triangle. [7.3]
Construct a triangle congruent to a given triangle. [7.3]
Classify triangles and use the terminology associated with triangle classifications. [7.3]
Use algebra to find the measures of angles in a triangle. [7.3]
Decide whether a pair of given triangles is similar. [7.4]
List all six angles for a given pair of triangles. [7.4]
List all six sides of a given pair of triangles. [7.4]
Given a right triangle, find the length of a missing side. [7.4]
Given similar triangles, find the length of one of the sides. [7.4]
Show that a given pair of triangles is similar. [7.4]
Solve applied problems using similar triangles. [7.4]
Evaluate a trigonometric ratio. [7.5]
Find the sine, cosine, and tangent for a given angle. [7.5]
Find sin-1
x, cos-1 x, and
tan-1 x. [7.5]
Solve applied problems using triangles. [7.5]
Know the terminology associated with right triangles. [7.5]
Work applied problems involving the golden ratio. [7.6]
Decide whether a figure is a Saccheri quadrilateral. [7.6]

Once again, see if you can verbalize (to yourself) how to do each of the listed types of problems. Work all of Chapter 7 Review Questions (whether they are assigned or not).

Work through all of the problems before looking at the answers, and then correct each of the problems. The entire solution is shown in the answer section at the back of the text. If you worked the problem correctly, move on to the next problem, but if you did not work it correctly (or you did not know what to do), look back in the chapter to study the procedure, or ask your instructor. Finally, go back over the homework problems you have been assigned. If you worked a problem correctly, move on the next problem, but if you missed it on your homework, then you should look back in the text or talk to your instructor about how to work the problem. If you follow these steps, you should be successful with your review of this chapter.

We give all of the answers to the Chapter Review questions (not just the odd-numbered questions), so be sure to check your work with the answers as you prepare for an examination.