Warm Up Add five more straight lines to make 10.
Warm Up Add five more straight lines to make 10.
Dec 13, 2015
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Warm UpAdd five more straight lines to make 10.
Point
Point A or
Point B
An exact position or location in a given plane.
Is represented by a dot and named with a capital letter.
Line The set of points between points P and Q in a plane and the infinite number of points that continue beyond the points.
Written as PQ$%%%%%%%%%%%%% %
P
Q
Line Segment
A line with two endpoints.Written as AB
Ray A line that has one endpoint and continues on forever in the opposite direction.
Circle
• The set of points on a plane at a certain distance, or radius, from a single point, the center
Angle
Made up of 2 rays joined together at a common point called a vertex.
The angle is
ABC
Perpendicular Line Two lines that intersect at a right angle (90°).Written as AB PQ
$%$%%$%%$%%$%%$%%$%%$%%$%%$%%$%%$%%$%%$% %$%
Parallel Line
Lines in a plane that either do not share any points and never intersect, or share all points.Written as AB PQ
$%$%%$%%$%%$%%$%%$%%$%%$%%$%%$%%$%%$%%$% %$%
Distance along a line
The linear distance between two points on a given line.
How far apart are the points on the line
segment?
How far apart are the points on the line
segment?
Hmmm…
Degrees
The unit of measure for angles.
Acute Angle
An angle measuring less than 90° but greater than 0°.
Obtuse Angle
An angle measuring greater than 90° but less than 180°.
Straight Angle
An angle measuring exactly 180°.
Adjacent Angles
Two angles that share a common vertex and side.
SIDE BY SIDE
Vertical Angles
Two angles directly across from each other. They share a common vertex.
h f
e
g
Linear Pair
Two adjacent angles that form a straight line.
1 2
Complementary Angles
Two angles that add up to 90 degrees.
12
3060
Supplementary Angles
Two angles that add up to 180°.
1 2
20160
A
B C
Practice(20 minutes)
*Use your vocabulary to help you…Check your Answers on the
Board!*
Pre-image
The original figure before undergoing a transformation.
Image
The new, resulting figure after a transformation
Isometry
A transformation in which the preimage and image are congruent.
Rigid transformations can also be referred to as an ISOMETRY.
Every segment is congruent to its image.
Transformations are called RIGID if every image is congruent to its preimage.
Which of the following are rigid transformations?
(Isometry)
* Translations
* preimage * image
(Slide your image over)
* Reflections
(Flip your image over)
* preimage * image
* Rotations(Turn your image
about a fixed point)
* preimage
* image
In the figure, XYZ → ABC by a reflection. Name the image of X.
AX
YZ
A
BC
Parallelogram MATH is transformed to Parallelogram LOVE by a rotation.What is the image of HT?
V
E
A
T
M
H
O
L
EV
Find the value of each variable, given that the transformation is an isometry.
72
x6
23 y10
4 ,12 yx
6x 72x 12
3y 2 10 3y 12
y 4
Congruent
Figures are congruent if they have the same shape, size, lines, and angles.
Similar Triangles
Triangles are similar if they have the same shape but have different sizes.
Corresponding angles are congruent and corresponding sides are proportional
A B
D C
E F
H G
Trapezoids ABCD and EFGH are similar ABCD ~ EFGH
List all congruent angles
HD
GC
FB
EA
Write the statement of proportionality
HE
DA
GH
CD
FG
BC
EF
AB
Determine if the polygons are similar. Justify your answer.
4
5EX 4
4
5
6
7
6
7NOTE: You must check for corresponding angles to be the same and for the sides to be proportional.
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