Transcript Problem 2.3 B1 B. Can you be sure that two triangles are congruent

Linear Algebra
Wednesday August 27
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for
homework
Answers for homework
Question 2 Check it Out
The graph is a straight line at an angle. The line
starts at 0,0. The information on the x-axis could
be the time the car has traveled. The information
on the y-axis could be the distance covered. You
might have mentioned that the car is moving at a
constant rate.
Learning Target
Students will investigate what is the smallest
number of side and/or angle measurements
needed to conclude that two triangles are
congruent.
Connect to Prior Understanding
What do we remember about Problem 2.2
Were all the triangles congruent?
What did we have to know at a minimum to
decide if the triangles were congruent?
2.3 Minimum Measurement
Congruent Triangles
In Problem 2.2 you might have noticed that it
is not necessary to move one triangle onto the
other to determine whether two triangles are
congruent.
2.3 Minimum Measurement Congruent
Triangles p. 35 in your book
Problem 2.3 A-E
Consider the conditions described in Questions
A-C. For each case, give an argument to
support your answer. If the conditions are not
enough to determine two triangles are
congruent, give a counterexample.
Problem 2.3 A
A. Can you be sure that two
triangles are congruent if
you know only
1. one pair of congruent
corresponding sides?
2. one pair of congruent
corresponding angles?
Counterexamples
Problem 2.3 B1
B. Can you be sure that two triangles are congruent if you know
only:
1. two pairs of congruent sides?
2. two pairs of congruent angles?
3. one pair of congruent corresponding sides and one pair of
congruent corresponding angles?
Problem B2
B. Can you be sure that two triangles are congruent if you know
only:
1. two pairs of congruent sides?
2. two pairs of congruent angles?
3. one pair of congruent corresponding sides and one pair of
congruent corresponding angles?
Problem 2.3 B3
B. Can you be sure that two triangles are congruent if you know
only:
1. two pairs of congruent sides?
2. two pairs of congruent angles?
3. one pair of congruent corresponding sides and one pair of
congruent corresponding angles?
Problem 2.3 C
C. Can you be sure that two triangles are congruent if you know
two pairs of congruent corresponding angles and one pair of
congruent corresponding sides as shown? Use your
understanding of transformation to justify your answer.
Problem 2.3 C
2. Can you be sure that two triangles are congruent if you know
two pairs of congruent corresponding sides and one pair of
congruent corresponding angles as shown?
Problem 2.3 D
Amy and Becky have different ideas about how to decide whether the condition
in Question C, Part (2) are enough to show triangles are congruent.
1.
Amy flips triangle GHI as shown. She says you can translate the triangle so
that HK and GJ. So all of the measures in triangle GHI match measure in
triangle JKL. Do you agree with Amy’s reasoning? Explain.
Problem 2.3 D
Amy and Becky have different ideas about how to decide whether the condition
in Question C, Part (2) are enough to show triangles are congruent.
2. Becky thinks Amy should also explain why the translation matches all the sides
and angles. She says that if you translate triangle GHI so that GJ, there will be
two parallelograms in the figure. These parallelograms show her which
corresponding angles and sides congruent. What parallelogram does she see?
How do these parallelograms help identify congruent corresponding sides and
angles?
Problem 2.3 E
1. Can you be sure that two triangles are congruent if you know three pairs of
congruent corresponding angles? Explain. Use tracing paper to see if this works.
Problem 2.3 E
2. Are there any other combinations of three congruent corresonding parts
what will guarantee two triangles are congruent? Make sketches to justify your
answer.
Problem 2.3 E
3. Suppose two triangles appear to be NOT congruent. What is the minimum
number of measures you should check to show they are NOT congruent?
Summarize
We know that triangles are congruent if we
know:
All sides are the same SSS (Side, Side, Side)
Two sides with an angle in between SAS
(Side, Angle, Side
Two angles with a side in between ASA
(Angle, Side, Angle)
Two angles and one side AAS (Angle, Angle,
Side)
Rate your understanding
Students will investigate what is the smallest
number of side and/or angle measurements
needed to conclude that two triangles are
congruent.
Homework
ACE questions starting on page 38 #7-12 and
page 3 of Mathematics warm-ups for CCSS,
grade 7