Name: Chapter 4 Guided Notes: Congruent Triangles. Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester

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1 Name: Chapter 4 Guided Notes: Congruent Triangles Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester

2 CH. 4 Guided Notes, page Apply Triangle Sum Properties triangle polygon sides vertices Classifying Triangles by Sides scalene triangle isosceles triangle equilateral triangle

3 Classifying Triangles by Angles CH. 4 Guided Notes, page 3 acute triangle obtuse triangle right triangle equiangular triangle interior angles exterior angles 4.1 Triangle Sum The sum of the measures of the interior angles of a triangle is 180. auxiliary lines 4.2 Exterior Angle The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. corollary to a theorem Corollary to the Triangle Sum The acute angles of a right triangle are complementary.

4 4.2 Apply Congruence and Triangles CH. 4 Guided Notes, page 4 congruent figures corresponding parts 4.3 Third Angles Reflexive Property of Congruent Triangles Symmetric Property of Congruent Triangles Transitive Property of Congruent Triangles If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. Properties of Congruent Triangles 4.4 Properties of Congruent Triangles For any triangle ABC, If If! ABC "! ABC.! ABC "! DEF, then DEF "! ABC!.! ABC "! DEF and DEF "! JKL then! ABC "! JKL.!,

5 4.3 Prove Triangles Congruent by SSS CH. 4 Guided Notes, page 5 Postulate 19 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.

6 CH. 4 Guided Notes, page Prove Triangles Congruent by SAS and HL included angle Postulate 20 Side-Angle- Side (SAS) Congruence Postulate right triangles 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. 1. legs- 2. hypotenuse- 3. side opposite- 4. sides adjacent- 4.5 Hypotenuse-Leg (HL) Congruence If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

7 CH. 4 Guided Notes, page Prove Triangles Congruent by ASA and AAS included side Postulate 21 Angle-Side-Angle (ASA) Congruence Postulate 4.6 Angle-Angle-Side (AAS) Congruence If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent. If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of a second triangle, then the two triangles are congruent. flow proof More Right Triangle Congruence s Leg-Leg (LL) Congruence If the legs of two right triangles are congruent, then the triangles are congruent. 1. SAS (included angle) Angle-Leg (AL) Congruence If an angle and a leg of a right triangle are congruent to an angle and a leg of a second right triangle, then the triangles are congruent. 1. AAS (non-included side) 2. ASA (included side) Hypotenuse-Angle (HA) Congruence If an angle and the hypotenuse of a right triangle are congruent to an angle and the hypotenuse of a second right triangle, then the triangles are congruent. 1. AAS (non-included side)

8 4.6 Use Congruent Triangles CH. 4 Guided Notes, page 8 congruent triangles Definition of Congruent Triangles (CPCTC) Two triangles are congruent if and only if their corresponding parts are congruent. This is also known as the Corresponding Parts of Congruent Triangles are Congruent. To show that a pair of corresponding parts of two triangles are congruent: 1. Prove the two triangles are congruent. 2. Use the definition of congruent triangles (CPCTC) to show the corresponding parts are congruent. What can we say about SSA and AAA? SSA SSA cannot be used as a proof of congruent triangles. See page 247. AAA AAA cannot be used as a proof of congruent triangles. AAA only proves the two triangles to be similar.

9 CH. 4 Guided Notes, page Use Isosceles and Equilateral Triangles 5 Vertex Angle parts of an isosceles triangle 6 Legs 7 Base 8 Base Angles 4.7 Base Angles 4.8 Converse of Base Angles Corollary to the Base Angles Corollary to the Converse of Base Angles If two sides of a triangle are congruent, then the angles opposite them are congruent. If two angles of a triangle are congruent, then the sides opposite them are congruent. If a triangle is equilateral, then it is equiangular. If a triangle is equiangular, then it is equilateral.

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