Chapter 4 Notes Congruent Polygons Congruent Polygons B

Chapter 4 Notes

Congruent Polygons: •

Congruent Polygons: B C F G A D E H Name ALL of the CONGRUENT angles and sides:

Congruent Polygons: B C F G A D E H Give the congruence Statement for the two figures:

Congruent Polygons: • L A M S E T P I R B

Congruent Polygons:

Congruent Triangles •

Congruent Triangles •

Congruent Right Triangles •

Congruent Triangles

Congruent Triangles

Words you need to know to do PROOFS: • Congruent • Vertical angles • Addition Property • Subtraction Property • Multiplication Property

Words you need to know to do PROOFS: • Division Property • Substitution Property • Symmetric Property • Reflexive Property • Third Angle Theorem • Midpoint

Words you need to know to do PROOFS: • Parallel • Alternate Interior • Alternate Exterior • Interior • Exterior • Perpendicular Bisector

Introduction to PROOFS: • 2 Column Proofs: STATEMENT REASONS 1. 2. 3.

Introduction to PROOFS: Write a proof for the following: STATEMENT 5 x + 3 = 18 REASONS 1. 2. 3.

Introduction to PROOFS: STATEMENT REASONS 1. 2. 3.

Introduction to PROOFS: STATEMENT REASONS 1. 2. 3.

Proving Triangles are Congruent • Steps: 1. If not given a picture, draw one. 2. Mark what you know on the picture (not what you are trying to prove). 3. Decide how you know the triangles are congruent (SSS, SAS, ASA, AAS). 4. State the given and the prove. 5. Complete the proof with the information.

Triangle Congruence Principles Side-Side (SSS) If the three sides of one triangle have the same measures as the three sides of a second triangle, then those triangles are congruent.

Side-Side (SSS) STATEMENT REASONS 1. Given 2. 3.

Side-Side (SSS) E B F C

Side-Side (SSS)

Triangle Congruence Principles Side-Angle-Side (SAS) If two sides and the included angle of one triangle have the same measure as two sides and the included angle of a second triangle, then those triangles are congruent.

Side-Angle-Side (SAS)

Side-Angle-Side (SAS)

Side-Angle-Side (SAS) T C G A B

Triangle Congruence Principles Angle-Side-Angle (ASA) If two angles and an included side of one triangle have the same measures as two angles and an included side of a second triangle, then those triangles are congruent.

Angle-Side-Angle (ASA) R o y J

Angle-Side-Angle (ASA) A C T N O STATEMENT REASONS 1. Given 2. 3.

Angle-Side-Angle (ASA) U B S STATEMENT REASONS 1. Given 2. 3. R

Triangle Congruence Principles Angle-Side (AAS) If two angles and a non-included side of one triangle have the same measures as two angles and a nonincluded side of a second triangle, then those triangles are congruent.

Angle-Side (AAS) J R O D A

Angle-Side (AAS) X Z Y W T STATEMENT REASONS 1. Given 2. 3.

ASS THERE IS NO CONGRUENCIES IN

Triangle Congruence Principles Hypotenuse-Leg (HL) If the hypotenuse and a leg of one RIGHT triangle have the same measures as the hypotenuse and a leg of a second RIGHT triangle, then those triangles are congruent.

Hypotenuse-Leg (HL) O B S X STATEMENT REASONS 1. Given 2. 3.

Hypotenuse-Leg (HL) T E H STATEMENT REASONS 1. Given 2. A 3.

Hypotenuse-Leg (HL) L G J K I H STATEMENT REASONS 1. Given 2. 3.