Transcript of Do Now Take out your compass and protractor. Put your 4.1/4.2 WS on your desk ready to be stamped....
- Slide 1
- Do Now Take out your compass and protractor. Put your 4.1/4.2
WS on your desk ready to be stamped. Draw LMN in your notebook.
Name the angles. Write an A at each angle. Name the sides. Write an
S at each side. Take out your compass and protractor. Put your
4.1/4.2 WS on your desk ready to be stamped. Draw LMN 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.
- Slide 2
- Error Analysis Compare your exit slip to Kathys
- Slide 3
- Are the Triangles Congruent? Congruence Shortcuts
- Slide 4
- Todays 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.
- Slide 5
- 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?
- Slide 6
- 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?
- Slide 7
- SSS Side-Side-Side Three pairs of congruent sides.
- Slide 8
- SAS Side-Angle-Side Two pairs of congruent sides and one pair
of congruent angles (angles between the pair of sides)
- Slide 9
- ASA Angle-Side-Angle Two pairs of congruent angles and one pair
of congruent sides (sides between the pairs of angles)
- Slide 10
- AAS Side-Angle-Angle Two pairs of congruent angles and one pair
of congruent sides (sides not between the pairs of angles)
- Slide 11
- SSA Side-Side-Angle Two pairs of congruent sides and one pair
of congruent angles (angles not between the pairs of sides)
- Slide 12
- AAA Angle-Angle-Angle Three pairs of congruent angles
- Slide 13
- 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.
- Slide 14
- 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.
- Slide 15
- In other words If you know this: Then you know this:
- Slide 16
- 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.
- Slide 17
- In other words If you know this: Then you know this:
- Slide 18
- 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.
- Slide 19
- In other words If you know this: Then you know this:
- Slide 20
- Angle Angle Side (AAS) Postulate If two angles and the
non-included side one triangle are congruent to two angles and the
non- included angle of another triangle, then these two triangles
are congruent.
- Slide 21
- In other words If you know this: Then you know this:
- Slide 22
- 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.
- Slide 23
- In other words If you know this: Then you dont know if the
triangles are congruent
- Slide 24
- 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.
- Slide 25
- In other words If you know this: Then you dont know if the
triangles are congruent
- Slide 26
- Practice Are these two triangles congruent? If so, why? Name
the congruent triangles. If not, why not?
- Slide 27
- Practice
- Slide 28
- Slide 29
- Congruency Shortcuts Review Shortcuts that show two triangles
are congruent SAS SSS ASA AAS Shortcuts that dont always work AA
SSA
- Slide 30
- Todays 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.
- Slide 31
- 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.
- Slide 32
- 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.