Download CONGRUENCE

CONGRUENCE
MS. SPRADLIN
GEOMETRY
2016-17
INTRODUCTION
• Today, we will move on to the topic of triangles, but this chapter will be all about determining if two
triangles are the same or what mathematicians like to say, congruent. I found a video on YouTube which
introduces most of the topics we will be covering in this chapter. While you are listening, write down
some of the topics that are mentioned. Keep this sheet and refer back to it throughout the chapter. By
the end, you should be able to explain almost everything that you wrote down.
VIDEOS
• https://www.youtube.com/watch?v=_L8u8io6n2A&feature=related
• https://www.youtube.com/watch?v=kSV5Plfbq48&spfreload=10
WHAT TOPICS CAN YOU REMEMBER FROM THE
VIDEOS?
• SAS
• SSS
• ASA
• AAS
• HL
• CPCTC
• Congruence
• Corresponding
TODAY
• We will be discovering the usefulness of congruence and corresponding parts
• There are specific notations to show congruence
• Congruent • Angle -
≅ - SAME
∠
• Triangle • Congruent sides on a triangle
• Write the letters of the triangles
clockwise starting with the lowerleft corner and wrapping around
the triangle
DEFINITIONS
• Congruence - Exactly equal in size and shape. Congruent sides or segments have the exact same length.
Congruent angles have the exact same measure. For any set of congruent geometric figures,
corresponding sides, angles, faces, etc. are congruent.
• Corresponding parts - Corresponding parts in a figure mean that the parts (angles or sides) are in the
same relative position in each of the figures.
HOW TO DEPICT CONGRUENT TRIANGLES
• There are specific notations to
show congruence.
YOU WILL NEED TO WRITE CONGRUENCE
STATEMENTS
When two triangles are congruent,
there are 6 facts that are true about
the triangles:
the triangles have 3 sets of
congruent (of equal length) sides and
the triangles have 3 sets of
congruent (of equal measure) angles.
NOTE: The
corresponding
congruent sides are
marked with small
straight line segments
called hash marks.
The corresponding
congruent angles are
marked with arcs.
IT IS TIME FOR YOU TO TRY
• You will be shown two triangles and they should shout out if you think that the triangles are congruent
to not congruent.
ARE THEY CONGRUENT OR NOT CONGRUENT?
Congruent
Congruent
Non-congruent
DANCING ACTIVITY
• Wander around the room during the music: https://www.youtube.com/watch?v=zq7Eki5EZ8o
• When the music stops go up to the student closest to you and determine whether or not your triangles
are congruent
• Go to the appropriate side of the classroom – I will check you for accuracy
• You will be asked to identify the parts that keep the triangles from being congruent
• We will do this three times! On the third time, you will switch triangles with someone before we dance!
NEXT!!!
• Time to do some examples!!!
R
EXAMPLE
Y
Q
?
10
95
• Find the length of line XZ, and find
the measure of angle Q
• Can you find the corresponding angles?
P
X
Z
?
REVIEW
• Congruence - Exactly equal in size and shape. Congruent sides or segments have the exact same length.
Congruent angles have the exact same measure. For any set of congruent geometric figures,
corresponding sides, angles, faces, etc. are congruent.
• Corresponding parts - Corresponding parts in a figure mean that the parts (angles or sides) are in the
same relative position in each of the figures.
CLOSURE
• You are to write a paragraph discussing what you have learned. The structure should start with a thesis
statement, include supporting sentences relevant to the thesis statement, and should end with a
statement that summarizes what was said.
• You will be graded on accuracy, grammar, and paragraph structure (Gardner’s: Linguistic)
• You will also have homework problems which you can work on if you get done early, which will be due
the next tomorrow.