Download Chapter Audio Summary for McDougal Littell

Chapter Audio Summary for McDougal Littell
Middle School Math, Course 2
Chapter 10 Geometric Figures
In Chapter 10 you saw how to classify and use properties of angles and triangles. You
saw how to classify quadrilaterals and other polygons. You also saw how to describe
transformations.
Turn to the lesson-by-lesson Notebook Review that starts on p. 499 of the textbook.
Review the Check Your Definitions section and the Use Your Vocabulary section, and
then look at the review examples that begin with the lesson numbers.
Lessons 10.1 and 10.2 Can you use angle relationships?
Important words and terms to know are: acute, right, obtuse, and straight angles;
complementary, supplementary, vertical and adjacent angles; congruent angles; plane;
parallel, intersecting, and perpendicular lines and corresponding angles.
The goals of lessons 10.1 and 10.2 are to classify angles, and identify special pairs of
angles and types of lines.
Read the example.
“Find a, the measure of angle ADC and b, the measure of angle DGF.”
For example a, to find the measure of angle ADC, look at the diagram and see that angles
ADC and ADB are supplementary angles. Supplementary angles have a sum of 180
degrees. So, you can write the equation: the measure of angle ADC plus the measure of
angle ADB equals 180 degrees. From the diagram, notice that the measure of angle ADB
is 105 degrees. So substitute 105 degrees in the equation for the measure of angle ADB.
Now subtract 105 degrees from each side of the equation to find that the measure of angle
ADC = 75 degrees.
For example b, to find the measure of angle DGF, use the fact that congruent
corresponding angles are formed when a line intersects two parallel lines. From the
diagram you can see that angle DGF and angle ADC are congruent corresponding angles.
So the measure of angle DGF = the measure of angle ADC = 75 degrees.
Now try Exercises 2 and 3. If you need help, go back to the worked-out examples on
pages 475, 476, and 479-481.
Lessons 10.3 and 10.4 Can you classify polygons?
Important words and terms to know are: acute, right, and obtuse triangles; congruent
sides; equilateral, isosceles and scalene triangles; quadrilateral; trapezoid;
McDougal Littell: Audio Summary
Geometric Figures
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Chapter Audio Summary for McDougal Littell
Middle School Math, Course 2
parallelogram; rhombus; polygon; pentagon; hexagon; heptagon; octagon; and regular
polygon.
The goals of lessons 10.3 and 10.4 are to classify triangles, quadrilaterals, and other
polygons.
Read the example.
“Classify the polygon shown.”
To classify the polygon that is shown in the diagram, notice its shape and read carefully
all the marks and labels that tell you the sizes of the angles and the relationship of the
sides. The shape is a triangle with two acute angles that measure 80 degrees, and one
acute angle that measures 20 degrees. The matching marks on two of the sides tell you
that these line segments are congruent. An isosceles triangle has at least two congruent
sides. An acute triangle has three acute angles, or less than 90 degrees, so this polygon is
an acute isosceles triangle.
Now try Exercises 4, 5, 6, and 7. If you need help, go back to the worked-out examples
on pages 484-486 and 494-496.
Turn to the lesson-by-lesson Notebook Review that starts on p. 524 of the textbook.
Review the Check Your Definitions section and the Use Your Vocabulary section, and
then look at the review examples that begin with the lesson numbers.
Lessons 10.5 and 10.6 Can you use properties of similar polygons?
Important words to know are: similar polygons and congruent polygons.
The goals of lessons 10.5 and 10.6 are to use properties of similar polygons and to find
lengths of the sides of polygons indirectly.
Read the example.
“Given that triangle BCD is similar to triangle FGH, a, name the corresponding sides and
corresponding angles, and b, find the length of FG.”
For example a, to name the corresponding sides and corresponding angles of the two
polygons, review the information you are given: The question states that triangle BCD is
similar to triangle FGH. Similar triangles have corresponding sides that are proportional.
Pair the sides that are proportional. The corresponding sides are BC and FG, CD and
GH, and DB and HF. Similar triangles have corresponding angles with the same
McDougal Littell: Audio Summary
Geometric Figures
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Chapter Audio Summary for McDougal Littell
Middle School Math, Course 2
measurement. Pair the angles that have the same measurement. The corresponding
angles are ∠B and ∠F, ∠C and ∠G, and ∠D and ∠H.
For part b, to find the length of the side FG, use proportions. Remember that a
proportion is an equation which shows that two ratios are equivalent. Write the
proportion that involves FG and the pair of corresponding lengths that you know: BC/FG
= DB/HF. Let the length of FG equal x and substitute the known lengths of sides BC,
DB, and HF: 10/x = 8/24. Next use the cross products property to write the equation as
10 times 24 is equal to x times 8. Now use inverse operations on each side to make the
coefficient of x equal to 1. Because x is multiplied by 8, the inverse operation is to divide
each side by 8. 10 times 24 divided by 8 is equal to 30; and x times 8 divided by 8 is
equal to 1 times x, or x. So x, the length of side FG, is equal to 30 cm.
Now try Exercise 2. If you need help, go back to the worked-out examples on pages
502, 503, 506, and 507.
Lessons 10.7 and 10.8 Can you describe transformations?
Important words and terms to know are: transformation, image, translation, reflection,
line of reflection, rotation, center of rotation, angle of rotation, line symmetry, line of
symmetry, and rotational symmetry.
The goals of lessons 10.7 and 10.8 are to describe and graph transformations in a
coordinate plane.
Read the example.
“Describe the translation using coordinate notation.”
Transformations, such as translation, reflection, and rotation, move a figure without
changing its size or shape. To describe the translation shown in the grid by using
coordinate notation, first look at the coordinates of each vertex of the original figure on
the right. Now look at the coordinates of the corresponding vertices in the translated
figure on the left. Notice that each point on the original figure is moved 7 units to the left
and 3 units down. So the x-coordinate of the translated figure is 7 units less and the ycoordinate is 3 units less than those coordinates in the original figure. In coordinate
notation, you write this translation as (x, y) translates to (x – 7, y – 3).
Now try Exercises 3, 4, and 5. If you need help, go back to the worked-out examples on
pages 511-513 and 518-520.
McDougal Littell: Audio Summary
Geometric Figures
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