Download If two sides and the included angle of one triangle are congruent to

Do Now
• Take out your compass and protractor.
• Put your 4.1/4.2 WS on your desk ready to be stamped.
• Draw ΔLMN in your notebook.
• Name the angles. L, M, N
• Write an “A” at each angle.
• Name the sides. LM, LN, MN
• Write an “S” at each side.
Error Analysis
• Compare your exit
slip to Kathy’s
Are the Triangles
Congruent?
Congruence Shortcuts
Today’s Objectives
• Determine whether two triangles are congruent.
• Discover that SSS and SAS are valid congruence
shortcuts but SSA is not.
• Discover that ASA and AAS are valid congruence
shortcuts but AAA is not.
• Use problem solving skills.
Intro
• A building contractor has just assembled two
massive triangular trusses to support the roof of a
recreation hall. Before the crane hoits them into
place, the contractor needs to verify that the two
triangular trusses are identical.
• Must the contractor measure and compare all six
parts of both triangles?
How much information would
it take?
• How many pieces of information does a triangle have?
• What if I asked everyone in here to draw a triangle? Would
everyone draw the same triangle?
• What if I told you one side had to be 5 cm?
• What if I told you that one side had to be 6 cm and one
angle 40 degrees?
• What is the least amount of information I would have to
give you for all of you to draw congruent triangles?
SSS
• Side-Side-Side
• Three pairs of congruent sides.
SAS
• Side-Angle-Side
• Two pairs of congruent sides and one pair of
congruent angles (angles between the pair of sides)
ASA
• Angle-Side-Angle
• Two pairs of congruent angles and one pair of
congruent sides (sides between the pairs of angles)
AAS
• Side-Angle-Angle
• Two pairs of congruent angles and one pair of
congruent sides (sides not between the pairs of
angles)
SSA
• Side-Side-Angle
• Two pairs of congruent sides and one pair of
congruent angles (angles not between the pairs of
sides)
AAA
• Angle-Angle-Angle
• Three pairs of congruent angles
Investigations
• We need to discover which cases turn out to be congruence
shortcuts and which do not.
• Rules
• Each person in your group must construct their own triangle.
• Your triangle must have the 3 pieces of information you were
assigned in order (side-angle-side for example)
• With your group, use the information given to you and see
if you come up with congruent triangles or different
triangles. Be ready to present your results.
Side Side Side (SSS) Postulate
• If three sides of one triangle are congruent to three
sides of another triangle, then these two triangles
are congruent.
In other words…
• If you know this:
• Then you know this:
Side Angle Side (SAS)
Postulate
• If two sides and the included angle of one triangle
are congruent to two sides and the included angle
of another triangle, then these two triangles are
congruent.
In other words…
• If you know this:
• Then you know this:
Angle Side Angle (ASA)
Postulate
• If two angles and the included side of one triangle
are congruent to two angles and the included side
of another triangle, then these two triangles are
congruent.
In other words…
• If you know this:
• Then you know this:
Angle Angle Side (AAS)
Postulate
• If two angles and the non-included side one
triangle are congruent to two angles and the nonincluded angle of another triangle, then these two
triangles are congruent.
In other words…
• If you know this:
• Then you know this:
Side Side Angle (SSA)
• If two sides and the included angle of one triangle
are congruent to two sides and the included angle
of another triangle, then these two triangles are
NOT NECESSARILY congruent.
In other words…
• If you know this:
• Then you don’t know if the triangles are congruent
Angle Angle Angle (AA)
• If two angles of one triangle are congruent to two
angles of another triangle, then these two triangles
are NOT NECESSARILY congruent.
In other words…
• If you know this:
• Then you don’t know if the triangles are congruent
Practice
• Are these two triangles congruent?
• If so, why? Name the congruent triangles.
• If not, why not?
Practice
Practice
Congruency Shortcuts Review
• Shortcuts that show two triangles are congruent
•
•
•
•
SAS
SSS
ASA
AAS
• Shortcuts that don’t always work
• AA
• SSA
Today’s Objectives
• Determine whether two triangles are congruent.
• Discover that SSS and SAS are valid congruence
shortcuts but SSA is not.
• Discover that ASA and AAS are valid congruence
shortcuts but AAA is not.
• Use problem solving skills.
Exit Slip
1. What type of information is given to you?
2. Are these triangles congruent? Why/why not?
1. Are these triangles congruent? Why/why not?
1. List the congruency shortcuts that always work.
Honors Exit Slip
For each figure to the right,
determine if the triangles are
congruent. If they are, write
a proof. If they are not,
explain why they are not.
1.
2.