Download Congruent Triangle Methods

WARM UP
APRIL 9TH
½ sheet
CONGRUENT FIGURES
Order Matters!
Just like SIMILAR FIGURES
Line up corresponding angles and sides
ABXY ≅ __________
HOW DO YOU SHOW CONGRUENCE?
Sides that are congruent?
Hash Mark
Angles that are congruent?
Arcs
CONGRUENT TRIANGLES
We will use the marks on a pair of triangles to determine whether
or not they meet one of our 5 methods.
Steps:
1. Mark any Vertical Angles or Reflexive Sides
2. Label ONE triangle with S (sides) and A (angles)
3. Look for a pattern.
- We must go around the triangle either clockwise or
counterclockwise
- You cannot skip more than 1 piece as you go around.
- Each triangle has 6 pieces, 3 sides and 3 angles
WHAT ARE VERTICAL ANGLES AND REFLEXIVE SIDES?
Vertical Angles form an ‘X’. Must be formed by two continuous lines
that cross.
WHAT ARE VERTICAL ANGLES AND REFLEXIVE SIDES?
Reflexive Sides are a shared side. The triangles will
appear as if they share a side.
FOLLOW THE STEPS
We can skip step 1 as there are no vertical angles or
reflexive sides.
Step 2: anything with a congruent piece, label as a side
or an angle using S or A for ONE TRIANGLE… if you
label both, it can get confusing.
STEP 3: PATTERN AND CHECK THE METHODS
As we go around the triangle I am only skipping 1 piece before
knowing another. I do side, side, side, where I am skipping the
angles.
This is an example of our 1st method. Side – Side - Side (SSS)
If the three sides of one triangle are congruent to the three sides of
another triangle, then the two triangles are congruent.
WHAT DOES THIS TELL US?
If AN ≅ LC, NP ≅ CK and PA ≅ KL, then ∆ LCK ≅ ∆ANP.
FOLLOW THE STEPS
What’s the pattern?
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 the
two triangles are congruent.
WHAT DOES THIS TELL US?
If CB ≅ EF, CA ≅ FD, and <C ≅ <F, then ∆ BCA ≅ ∆ EFD.
WHAT METHOD PROVES THE TRIANGLES CONGRUENT?
“NOT POSSIBLE” COULD BE YOUR ANSWER.
WHAT ARE THE STEPS FOR CONGRUENT
TRIANGLE METHODS?
Steps:
1.Mark any __________ Angles or ____________
Sides
2.__________ ONE triangle with ___ (sides) and
___ (angles)
3.Look for a ________ and decide on a ________.
FOLLOW THE STEPS…
What’s the pattern?
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 the two
triangles are congruent.
WHAT DOES IT TELL US?
If <B ≅ <K, <A ≅ <J, and BA ≅ KJ, then ∆ BAC ≅ ∆ KJL.
FOLLOW THE STEPS…
What’s the pattern?
ANGLE – ANGLE – SIDE (AAS) THEOREM
If two angles and the non-included side of one
triangle are congruent to two angles and the
non-included side of another triangle, then the
two triangles are congruent.
WHAT DOES IT TELL US?
If <R ≅ <A, <RDE ≅ <ADE, and DE ≅ DE,
then ∆ RDE ≅ ∆ ADE.
FOLLOW THE STEPS…
What’s the pattern?
HYPOTENUSE – LEG (HL) THEOREM
If the hypotenuse and one leg of one right
triangle are congruent to the hypotenuse and
a leg of another right triangle, then the two
triangles are congruent.
WHAT DOES IT TELL US?
If CB ≅ RQ, CA ≅ RP, and <B and <Q are right
angles, then ∆ ABC ≅ ∆ PQR.
TWO METHODS WE CANNOT USE
AAA: congruent angles only guarantees similarity. Think
about all equilateral triangles, the angles all measure
60 but the sides can be any length as long as they
are the same on a given triangle.
SSA (or its reverse): with an angle that isn’t included,
we can swing one side out to create a long 3rd side or
push it in to create a really short 3rd side.
NO TRANSPORTATION!!!!!!
No AAA
No Donkeys (SSA)
ARE THE TWO TRIANGLES CONGRUENT? WHAT METHOD?
HOMEWORK
Worksheet