DO NOW:

• Pick up the two papers off the back table

• Get your HW out and the blue calendar for Ms.

Taylor to stamp• Complete the half sheet of

paper from the back table

CONGRUENT

TRIA

NGLE

METHODS

SSS, SA

S, ASA

, AAS

{AN

D} H

L

CONGRUENT FIGURES

Order Matters!Just like SIMILAR FIGURESLine 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.

EXAMPLE 1 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.

EXAMPLE 2 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? REVIEW

Steps:1.Mark any Vertical Angles or

Reflexive Sides2.Determine how many pairs you

have of each3.Look for the order and decide on a

method.

EXAMPLE 3: 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.

EXAMPLE 4 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.

EXAMPLE 5 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