Download Geo G-CO Exploring SAS, ASA, AAS

Transitioning to Iowa Core Mathematics
Title: Exploring Congruent Triangles (Day 2: SAS, ASA, AAS)
Grade: 9-10
Author(s): Lischwe
Iowa Core Standards for
Mathematical Practices
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1. Making sense of problems
2. Reason abstractly
3. Construct viable arguments
4. Model
5. Use tools
6. Attend to precision
7. Structure
8. Repeated reasoning
Place * next to portions of lesson where students
use practice standards.
Student Outcome
I can decide if two triangles will be congruent based
on their sides or angles.
Purpose/ Learning Goals
Comparing parts of triangles can help you decide if they
are congruent or not. Today, we will construct our own
triangles and use them to discover when triangles are
congruent and when they are not.
Grouping Strategies
Partners
LESSON SEQUENCE
(Include plans for adjustments to accommodate all learners)
Launch
Activities
-Review the previous day’s activity:
-If all 3 sides of two triangles are
congruent, are the triangles
congruent?
-If all 3 angles of two triangles are
congruent, are the triangles
congruent?
-Go through a series of diagrams with
certain sides and angles marked
congruent, and ask them to
identify if they show SSS, AAA,
SAS, SSA, ASA, or AAS.
Notes
Materials
-Pre-made problems
with certain angles
and sides marked
congruent
-Have them see if they can figure it
out without telling them. Make
sure they understand, though,
before moving on to the “explore”
-Tell students that out of the four they
haven’t looked at yet, some of
them guarantee that triangles are
congruent and some of them
don’t.
Explore
Activities
-“Congruent Triangle Shortcuts, Day
2” (Attached)
Notes
-The task is pretty open-ended, so
students may want to know the
right answers immediately. Don’t
tell them any answers until the
“Summarize”
Materials
-Ruler
Summarize
Activities
-Review the worksheet with everyone.
SAS, ASA, and AAS guarantee
congruence, but SSA does not.
-Show them with two yardsticks how
Notes
Materials
-Example problems
for congruent
triangles
if two sides are fixed but the angle
in between them can change,
then the triangles aren’t
necessarily congruent. This shows
why it must be SAS, and not SSA,
for the triangles to be congruent.
-Show them some basic examples
(maybe even the same ones as
from the launch) and ask them to
tell whether they are congruent
and why
-The “why” can just be SSS, ASA, etc.
Congruent Triangle Shortcuts: Day 2
1) Use your ruler to construct a triangle with two of the sides measuring 4 inches and 5 inches. The third side does
not matter. The angle in between the 4-inch and 5-inch sides must be 30o.
2) Compare your triangle with the triangles of your group-mates. Are they all congruent?
3) Based on what is congruent, do these triangles show SSS, AAA, SAS, SSA, ASA, or AAS?
4) Do you think this guarantees that two triangles are congruent?
5) Study this diagram. How many sides are congruent? How many angles are congruent?
3cm
4cm
4cm
3cm
32o
6cm
32o
2cm
6) Based on what is congruent, do these triangles show SSS, AAA, SAS, SSA, ASA, or AAS?
7) Does this guarantee that triangles are congruent?
8) Yesterday, you learned that if two triangles have three pairs of congruent angles, they are still not necessarily
congruent. This is because you can stretch out the sides while keeping the angles the same.
70o
70o
40o
40o
70o
70o
If the side in between the two 70o angles was fixed at 3 inches in both triangles, would that be enough to prove
that the triangles are congruent? Explain your reasoning.
9) If the top side between the 70o angle and the 40o angle was fixed at 5 inches in both triangles, would that be
enough to prove that the triangles are congruent? Explain your reasoning.
10) Identify the sequence of letters that matches this diagram: SSS, AAA, SAS, SSA, ASA, AAS. Does this guarantee
that two triangles are congruent?
70o
70o
3cm
3cm
70o
70o
11) Identify the sequence of letters that matches this diagram: SSS, AAA, SAS, SSA, ASA, AAS. Does this guarantee
that two triangles are congruent?
5cm
5cm
70o
70o
70o
70o