Download Lesson 2-3 Multiplying Rational Numbers

Lesson 6-1 Line and Angle Relationships
Classify each angle or angle pair using
all names that apply and name the
missing measures.
1.
2.
3.
32
4.
128
Angles – Acute < 90
Right = 90
Obtuse > 90
Straight = 180
Special Pairs of Angles:
Vertical – Opposite Adjacent– Angles
angles that
that are
are
next to
congruent
each
other.
Complementary
Supplementary
Add up to
Add up to
90
180
Lines:
Perpendicular –
lines that intersect
at right angles (⊥).
Parallel – lines that
never intersect or
5.
152
cross (∥).
Transversal – a line that
intersects two or more
other lines.
6.
63
Alternate Interior Angles – opposite sides of
the transversal, inside the parallel lines; 3
 6, 4  5.
Alternate Exterior Angles - opposite sides of
the transversal, outside the parallel lines;
1  8, 2  7.
Corresponding Angles – In the same place
but on a different set of angles;
1  5, 2  6, 3  7, 4  8.
Glencoe Math App & Con (2006) – Course 3
Lesson 6-2 Triangles and Angles
Classify the following triangles by their
angles and their sides.
1.
2.
Polygon – closed figure formed by 3 or
more line segments.
Triangle – a polygon with 3 line
segments.
Classifications by Angles:
Acute
Obtuse
3.
4.
3 acute
angles
Find the value of x in each triangle:
5.
6.
Right
1 obtuse
angle
Classifications by Sides:
Scalene
Isosceles
No congruent
sides
1 right
angle
Equilateral
2 congruent
sides
1 right
angle
Sum of the angles of a triangle
always = 180°.
7.
Find the value of x in ABC if
mA = 80°, mB = 54°, and mC = x°.
8.
80 + 54 + x = 180
134 + x = 180
-134
-134
x = 46°
Glencoe Math App & Con (2006) – Course 3
Lesson 6-2A Sides That Form a Triangle
Will the following sides for a triangle?
1. 9, 16, 4
Three sides will form a triangle if…
1) The 2 smaller numbers subtracted is less
than the largest number.
2) The same two numbers added together
are greater than the largest number.
x–y<z<x+y
2. 11, 8, 9
Will 7, 9, and 24 form a triangle?
9 – 7 < 24 < 9 + 7
2 < 24 < 16
3. 12, 11, 16
Yes or No?
If the answer is no, then they won’t form a
triangle.
4. 6, 17, 11
If the answer is yes, then they will.
5. 9, 12, 16
Glencoe Math App & Con (2006) – Course 3
Lesson 6-3 Special Right Triangles
Find the length of each missing side.
1.
c = 2a or a = ½ c
a = side
opposite the
30º angle
2.
The sides of a triangle whose angles
measure 30º, 60º, 90º have a special
relationship. The hypotenuse is always
twice as long as the sides opposite the 30º
angle. Then us Pythagorean Theorem to
find the 3rd side.
3.
4.
a=b
A 45º - 45º right triangle is also an isosceles
triangle because two angle measures are the
same. Thus, the legs are always congruent.
5.
6.
Glencoe Math App & Con (2006) – Course 3
Lesson 6-4 Classifying Quadrilaterals
Classify each quadrilateral using the
name that best describes it.
1.
Quadrilateral – a polygon with 4
straight sides and 4 angles.
Copy concept map on pg 273.
2.
Angles of a quadrilateral = 180º.
3.
Find the value of x.
4.
5.
6.
7.
Glencoe Math App & Con (2006) – Course 3
Lesson 6-5 Congruent Polygons
Determine whether the polygons shown
are congruent. If so, name the
corresponding parts and write a
congruency statement.
1.
Congruent – two figures that have the
same size and shape.
Corresponding Parts – parts of
congruent polygons that “match.”
If 2 polygons are congruent;
1) Corresponding sides are equal.
2) Corresponding angles are equal.
2.
Congruency Statement:
Angles: The arcs indicate that A ≅ D, B
≅ F, and C ≅ E.
Sides: The sides measurements indicate that
AB ≅ DF , AC
In the figure DFG  TRE .
Find each measurement.
≅
DE , and BC ≅ AB .
Finding missing measures
3. mR
4. RT
5. mE
Find JL.
MN corresponds to JL . So, MN ≅ JL .
Since MN = 2 cm, JL = 2 cm.
Find mH.
According to the congruence statement, B
and H are corresponding angles. So, B ≅
H. Since mB = 60º, mH = 60º.
Glencoe Math App & Con (2006) – Course 3
Lesson 6-6 Symmetry
Determine whether the figures have line
symmetry. If it does, draw all the lines
of symmetry. If it doesn’t, write none.
Determine whether each figure has
rotational symmetry. Write yes or no. If
yes, name it’s angles of rotation.
1.
2.
Line Symmetry – a figure can be
folded so that one half of the figure
coincides with the other half.
Reflection – when the image is the
mirror image of another.
Line of Symmetry – the line. Also can
be called the Line of Reflection.
B
Line of Symmetry
3.
4.
5. Determine whether the sun
symbol of New Mexico has
rotational symmetry.
Rotations – spins. If a figure can be
turned less than 360° about its center
and still look like the original.
The degrees of rotational symmetry;
45°, 90°, 135°, 180°, 225°, 270°, and
315°.
Glencoe Math App & Con (2006) – Course 3
Lesson 6-7 Reflections
1. Reflect RST over the y-axis.
2. Reflect ABC over the x-axis.
Steps in Drawing a Reflection:
Step 1 - Count the number of units
between each vertex and the line of
reflection.
Step 2 - To find the corresponding
point for vertex A, move along the
line, through vertex A, perpendicular
to the line of reflection until you are 3
units from the line on the opposite
side. Draw a point and label it A’.
Repeat for each vertex.
3. Graph quadrilateral EFGH with
vertices E(-4, 4), F(3, 3), G(4, 2), and
H(-2, 1). Then graph the image of EFGH
after a reflection over the x-axis and
write the coordinates of its vertices.
4. Graph trapezoid ABCD with vertices
A(1, 3), B(4, 0), C(3, -4), and D(1, -2).
Then graph the image of ABCD after a
reflection over the y-axis and write the
coordinates of its vertices.
Step 3 – Connect the new vertices to
form quadrilateral A’B’C’D’.
Glencoe Math App & Con (2006) – Course 3
Lesson 6-8 Translations
Draw the image of the figure after the
indicated translation.
1. 5 units right and 4 units down.
When a figure is translated:
1) Every point is moved the same
distance in the same direction.
2) The translated figure is congruent
to the original figure and has the
same orientation.
Step 1 – Move each vertex 2 units
right, along the horizontal grid line,
and then move up 3 units along the
vertical grid line.
2. 4 units right and 1 unit up.
3. Graph ABC with vertices A(-2, 2),
B(3, 4), and C(4, 1). Then graph the
image of ABC after a translation 2
units left and 4 unit down. Write the
coordinates of its vertices.
Step 2 – Connect the new vertices to
create the new figure. Be sure to
put the symbol beside each letter to
show that it is a translation.
Glencoe Math App & Con (2006) – Course 3
Lesson 6-9 Rotations
1. Graph ABC with vertices A(1, 1),
B(3, 4), and C(4, 1). Then graph the
image of ABC after a rotation of 180°
about the origin, and write the
coordinates of its vertices.
Rotation – moves a figure about a
central point.
Step 1 – Graph trapezoid ABCD.
Grap
2. Copy and complete the quilt square
by rotating the design 180° about the
given point. What does the completed
figure resemble?
Step 2 – To find the corresponding
point for vertex A, draw a line
segment between A and the origin.
Then draw a second line segment
starting at the origin that is the same
length as the first segment and forms a
90° angle with the first segment.
Draw a point at the end of the second
segment and label it A’.
Step 3 – Repeat for vertex B’.
Step 4 – Repeat for vertices C’ and D’.
Glencoe Math App & Con (2006) – Course 3
Lesson 6-9b Tessellations
Complete each “Your Turn” in
each activity on page 304 and 305.
Tessellation – a tiling made up of
copies of the same shape or shapes
that fit together without gaps and
without overlapping.
Transformations – movement of
geometric figures.
Translation - moving a piece cut out,
from one side of a regular shape, to
the opposite side.
Rotation – moving a piece cut out,
rotating around one axis (to the left or
the right).
Glencoe Math App & Con (2006) – Course 3