Unit 3 Notes Congruent Triangles

Geometry/Trigonometry Unit 3: Congruency Notes

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(1) Page 166 #1 - 14 all (2) Page 166 #19 ? 26 and 31 ? 34 (3) Page 172 #1 - 15 all (4) Page 172 - 173 #19 ? 22 All, 24 ? 30 EVEN, 31 - 34 ALL (5) Page 180 #1 - 12 ALL; 15 and 16 (6) 4.3 Practice Worksheet (7) Page 186 #1 - 15 ODD (8) Page186 #2 - 16 EVEN (9) Page189 #1- 20 ALL (10) Page 193-194 #1 - 21 ODD Skip 11 and 13 (11) Page 193-194 #2 - 22 EVEN Skip #12 (12) Page199 - 200 #1 - 13 ODD and 19 (13) Page 199 - 200 #2 - 14 EVEN and 18 (14) PROOFS (15) PROOFS (16) Page209 - 211 #2 - 14 EVEN, 19 and 20; 34 and 36 (17) Page 213 #1 - 20 ALL

Geometry Notes 4.1 Exploring Congruent Triangles

Definition of congruent triangles ? If , then there is a _______________________ between their angles and sides such that corresponding ___________________ are congruent and corresponding ____________________ are congruent. The notation indicates the congruence and the correspondence as shown below.

B

Q

A

Corresponding angles are: _________ _________ _________

C

R

P

Corresponding sides are:

_________ _________ __________

A triangle can be classified by relationships among its _____________ or among its _____________. Classification by Sides: (1) An __________________________ triangle has__________________ congruent sides. (2) An__________________________ triangle has _________________________ congruent sides. (3) A _______________________ triangle has _____________________ congruent.

Classification by Angles: (1) An ________________ triangle has _____________________ acute angles. If these angles are ______________________________, then the triangle is also ______________________.

(2) A ___________________ triangle has ____________________________________ angle.

(3) An __________________________ triangle has ________________________________ angle.

Anatomy of a triangle:

Theorem 4.1 - Properties of Congruent Triangles: 1. Every triangle is congruent to itself (Reflexive) 2. If , then (Symmetric) 3. If and , then . (Transitive) Geometry Notes 4.2 Angles of a Triangle Triangle ? ____________________ which refers to the angles ____________ the triangle, aka the _______________________.

***____________________ ? the angles that are _________________to the _____________________of the triangle.*** Name the Interior Angles: Name the Exterior Angles:

Theorem 4.2 Triangle Sum Theorem: The sum of the measures of the interior angles of a triangle is 180?

Theorem 4.3 Third Angles Theorem: If two angle of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

Theorem 4.4: The acute angles of a right triangle are complementary.

Theorem 4.5 Exterior Angles Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote (nonadjacent) interior angles.

Theorem 4.6 Exterior Angle Inequality: The measure of an exterior angle of a triangle is greater than the measure of either of the two remote (nonadjacent) interior angles.

4.3 and 4.4 Vocabulary Preview Included Angle: ________________________________________________________________________ Included Side: _________________________________________________________________________

: - :

: - :

Geometry Notes 4.3 Proving Triangles are Congruent Postulate 17 Side-Side-Side (SSS) Congruence Postulate: If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Postulate 18 ? Side ? Angle ? Side (SAS) Congruence Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

Geometry Notes 4.4 More Ways to Prove that Triangles are Congruent

Postulate 19 ? Angle ? Side ? Angle (ASA) Congruence Postulate: If two angles and the included side of one triangle are congruent to two angles and an included side of a second triangle, then the triangles are congruent.

Theorem 4.7 Angle ? Angle ? Side (AAS) Congruence Theorem: If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent.

4.3 and 4.4 Recap Ways to Prove Congruent Triangles

Ways Not to Prove Congruent Triangles

Geometry Notes 4.5 CPCTC

By definition, two triangles are congruent if and only if (IFF) their __________________________ are congruent. This is sometimes abbreviated as CPCTC.

C___________________________ P___________________________ of C___________________________ T___________________________ are C___________________________ Example Proof Using CPCTC:

STATEMENTS

REASONS

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