Download Are the triangles congruent?

Warmup
Are the triangles congruent? Explain why or why not. Write the
congruence statements for each pair of sides or angles in your
explanation.
A
Given: C is the midpoint of both 𝑨𝑬 and 𝑩𝑫.
C
D
B
E
Are the triangles congruent? Explain why or why not. Write the
congruence statements for each pair of sides or angles in your
explanation.
Given: C is the midpoint of both 𝑨𝑬 and 𝑩𝑫.
A
C
D
B
E
• 𝑨𝑪 ≅ 𝑬𝑪 because C is the midpoint of 𝑨𝑬.
• 𝑩𝑪 ≅ 𝑫𝑪 because C is the midpoint of 𝑩𝑫.
• ∠𝑨𝑪𝑩 ≅ ∠𝑬𝑪𝑫 because vertical angles are congruent.
• So the triangles are congruent by SAS.
Let’s Review!
◦We can prove triangles are congruent by
◦ Rigid Motions
◦ Knowing all sides AND angles are congruent
◦What we learned yesterday was that we do
not need to know that all sides are
congruent and all angles are congruent to
prove two triangles are congruent.
Let’s Review
◦There are shortcuts we can use to prove
triangles are congruent!
◦We can prove triangles are congruent if
◦ We know all sides are congruent (SSS)
◦ We know two sides are congruent and the included
angle is congruent (SAS)
A Video…
https://www.khanacademy.org/math/geometry/congruence/trianglecongruence/v/more-on-why-ssa-is-not-a-postulate
SSA is not a shortcut!
Write down when it is not a shortcut.
Remember: For right triangles…
HL Congruence (Special Case
of SSA)
Example of HL Congruence
Which rigid
motion???
Objective:
Explore Triangle
Congruence
Triangle Angle Sum Theorem
All of the angles in a triangle sum to 180 degrees
Discuss with your trio
Do you think that AAA works as a shortcut?
◦In other words, if we know all of the angles
of two triangles are congruent, do we
know that the two triangles are
congruent?
AAA is not a shortcut!
Write down why it is not a shortcut.
An included side is the common side
of two consecutive angles in a polygon.
The following postulate uses the idea of
an included side.
ASA Activity
Construct a triangle with a 3 inch straw and angles given to
you. The three inch straw will be your included side. You will
have to cut up the straw to construct the other two side
lengths.
Compare your triangle with the triangles made by other in
your group. Is it possible to construct different triangles
from the same three parts? Are your triangles congruent?
ASA Congruence
Example of ASA Congruence
Determine if you can use ASA to
prove NKL  LMN. Explain.
By the Alternate Interior Angles Theorem. KLN  MNL
and KNL  MLN. NL  LN by the Reflexive Property. So
ASA can be applied.
SAA Activity
Construct a triangle from the two angles given and
a 3 inch straw. The 3 inch straw should be the unincluded side. You will have to cut up a straw to
come up with your other two side lengths.
Compare your triangle with the other triangles at
your table. Is it possible to construct different
triangles from the same three parts, or will all the
triangles be congruent?
AAS Congruence
Example of AAS Congruence
Given: 𝑱𝑳 𝒃𝒊𝒔𝒆𝒄𝒕𝒔 ∠𝑲𝑳𝑴
Determine if you can use AAS to
prove that the triangles are
congruent.
Write Down all the Three Letter
Variations of the Combinations of
the letters A and S
For example: SSS
Circle which ones work as shortcuts and
which ones do not work as shortcuts
Group the ones that mean the same
thing!
For example: AAS is the same as SAA
Works As a Shortcut
Does Not Work As a Shortcut
SSS
SAS
HL
ASA
AAS/SAA
SSA *
AAA
*works in some cases
Homework
ASA pg. 1007-1008 (3-6)
AAS pg. 1060 (1-7)