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Transcript
5.1 Homework Quiz
1. What are the 4 ways of knowing that we discussed last
time in class?
2. Find the measure of the missing angle in the diagram
below assuming the figure is made up of 2 lines:
108
?
1. What are the minimal conditions necessary to identify
that two triangles are congruent (one is just a
transformation of the other)? Or in other words, what
are the triangle congruence theorems?
Do you See What I See
Last time we looked at the figure below and
imagined how it was constructed and then I
showed you how it was constructed. The final
diagram we said suggested that the sum of the
angles of a triangle is 180 degrees.
What can you say about the triangle in the following
diagram?
What convinces you that you can make this claim?
Did you make any assumptions with this claim?
List several conjectures that you believe are true
about the triangles, quadrilateral, and diagonals
of the quadrilateral in the figure below.
What have we proven/accept as
axioms?
Properties of the transformations: rotation,
reflection, translation
Any angles that together create a straight line, sum
to 180 degrees.
Triangle congruence theorems
Pythagorean Theorem
Conjectures to be Proven
1. The base angles of isosceles triangles are
congruent
1. The diagonals of a rhombus bisect each other
1. The diagonals of a rhombus are perpendicular
*Trick: Prove different triangles are congruent.
What steps were used to create this diagram?
Hannah and Abi were doing their math homework
together. One of the questions asks them to prove the
following statement.
The points on the perpendicular bisector of a segment are
equidistant from the endpoints of the segment.
They thought this diagram would be helpful for
justification along with descriptions.
Given information
Just need to pick an
arbitrary point C on l.
Restating goal
Construct line segments AC and
BC to create triangles.
Thinking. Not necessary for the argument
It might be easier to order these statements
by talking about the angle measure in
between the two sides.
We need to name the two triangles that are
congruent
A and B are equidistant from C
What have we proven:
-Properties of the transformations
-Any angles that create a straight line total 180 degrees.
-Triangle congruence theorems
-Pythagorean Theorem
*The base angles of isosceles triangles are congruent.
*The diagonals of a rhombus bisect each other.
*The diagonals of a rhombus are perpendicular.
*The points on the perpendicular bisector of a segment
are equidistant from the endpoints of the segment.