Download Transformations, Congruence, and Similarity

UNIT 1
GEOMETRIC TRANSFORMATIONS
STANDARD: M8G.5
• Students will understand and
apply the properties of parallel
and perpendicular lines and
understand the meaning of
congruence.
ELEMENT: M8G.5
•Investigate characteristics
of parallel and perpendicular
lines both algebraically and
geometrically
.
ELEMENT: M8G.5
•Apply properties of angle
pairs formed by parallel
lines cut by a transversal.
UNIT 1 VOCABULARY (CH. 6 PG 256)
• Acute Angle – measures less than 90°.
• Right Angle – measures equal to 90°.
• Obtuse Angle – have measures between
90° and 180°.
• Straight Angle – measures equal to 180°.
UNIT 1 VOCABULARY CONT.
• Vertical Angles – opposite angles
formed by intersecting lines. Vertical
angles are congruent.
• Adjacent Angles – have the same
vertex (angle), share a common side,
and do NOT overlap.
UNIT 1 VOCABULARY CONT.
• Complimentary Angles – angles whose sum of their
measures is equal to 90°. If you put the angles
together, the angles should form a right angle.
• Supplementary Angles – angles whose sum of their
measures is equal to 180°. If you put the angles
together, the angles should form a straight angle.
UNIT 1 VOCABULARY CONT.
• Perpendicular Lines - lines that
intersect at right angles.
• Parallel Lines – two lines in a plane that
never intersect or cross.
• Draw the diagram on page 257.
UNIT 1 VOCABULARY CONT.
• Transversal – a line that
intersects two or more lines.
• Draw diagram on page 258.
COMPLIMENTARY ANGLES
PARALLEL LINES CUT BY A TRANSVERSAL
ANGLE RELATIONSHIPS
GEOMETRIC CITY
ANGLE RELATIONSHIPS
REVIEW YOUR NOTES
• Acute and obtuse angles
• Interior and exterior angles
• Vertical angles
• Corresponding angles
• Same side angles
• Complementary and Supplementary angles
COMBINING LIKE TERMS
• Term – the part of an expression the is separated by a +
or – sign.
• Variable – a symbol used to represent a quantity that
can change.
• Coefficient – the number that is multiplied by a variable.
• Constant – a term without a variable; the value never
changes.
• Like terms – terms that have the same variable(s) raised
to the same powers(s).
COMBING LIKE TERMS
DISTRIBUTIVE PROPERTY
DISTRIBUTIVE PROPERTY
COORDINATE SYSTEM VOCABULARY
• Coordinate plane – formed by two
number lines that form right angles
and intersect at their zero points.
• Y-axis – the vertical number line.
• X-axis – the horizontal number line.
COORDINATE SYSTEM VOCABULARY CONT.
• Origin – The point of intersection of the two number
lines. The ordered pair for the origin is (0,0).
• Quadrants – The number lines separate the
coordinate plane into four quadrants (sections).
• Ordered Pair – Any point on the coordinate plane can
be graphed by using a pair of numbers. The first
number in the ordered pair is the x-coordinate. The
second number in the ordered pair is the ycoordinate. (x,y).
COORDINATE SYSTEM VOCABULARY CONT.
• X-coordinate – The first number in an
ordered pair. Also called the abscissa.
• Y-Coordinate – The second number in
an ordered pair. Also called the
ordinate.
REVIEW OF COORDINATE SYSTEM
REVIEW OF COORDINATE SYSTEM
STANDARD: M8G.1
• Verify experimentally the congruence
properties of rotations, reflections, and
translations: lines are taken to lines and line
segments to line segments of the same
length; angles are taken to angles of the
same measure; parallel lines are taken to
parallel lines.
VOCABULARY
• Transformation – mapping of a
geometric figure.
• Reflection – mirror image produced by
flipping a figure over a line.
• Line of Reflection – the line an image is
flipped over.
TRANSLATIONS
TRANSLATIONS
TRANSLATIONS
TRANSLATION TEST PRACICE
• http://www.regentsprep.org/regents/math/geometry/GT2/PracT.htm
ROTATIONS
COMPLETE PACKET (PACKET WILL BE YOUR TEST GRADE)
COMPLETE TRANSFORMATION ARTWORK (FOLLOW
INSTRUCTIONS ON PAGE)
COMPLETE TRANSFORMATION AIRPLANE (FOLLOW
INSTRUCTIONS ON PAGE)
• Properties preserved (invariant) under a rotation:
1. distance is preserved (lengths of segments are the
same)
2. angle measures (remain the same)
3. parallelism (parallel lines remain parallel)
4. colinearity (points stay on the same lines)
5. midpoint (midpoints remain the same in each
figure)
6. orientation (lettering order remains the same)
REFLECTIONS
WRITE QUESTION AND ANSWER IN MATH JOURNAL
• How would you reflect an image over the xaxis?
• How would you translate a figure T(3,-5)?
• How would you rotate a point R(90)?
• How would you rotate an image R(270)?
• How would you rotate an image R(-90)?
TRANSFER TO MATH JOURNAL
• Dilation - A dilation is a transformation
(notation ) that produces an image that is
the same shape as the original, but is a
different size. A dilation stretches or
shrinks the original figure. The
description of a dilation includes the
scale factor (or ratio) and the center of
the dilation.
SCALE FACTOR DEFINITION
• In two similar geometric figures, the ratio
of their corresponding sides is called the
scale factor. To find the scale factor,
locate two corresponding sides, one on
each figure. Write the ratio of one length
to the other to find the scale factor from
one figure to the other.
•MGSE8.G.3 Describe the
effect of dilations,
translations, rotations, and
reflections on two‐
dimensional figures using
coordinates.
MATH MASHUP
DISCOVERY EDUCATION
• https://app.discoveryeducation.com/learn/videos/5792d4bc-4fc1-4267-bdee-f151af95dc1d
TRANSFER TO MATH JOURNAL
• A tessellation of a flat surface is the tiling of
a plane using one or more geometric
shapes, called tiles, with no overlaps and no
gaps. In mathematics, tessellations can be
generalized to higher dimensions and a
variety of geometries. A periodic tiling has a
repeating pattern.