Triangle Congruency

Classifying Triangles by Sides Equilateral Triangle 3 congruent sides Isosceles Triangle At least 2 congruent sides Scalene Triangle No congruent sides

Classifying Triangles by Angles Acute Triangle Equiangular Triangle Right Triangle Obtuse Triangle 3 acute angles 3 congruent angles 1 right angle 1 obtuse angle Note: An equiangular triangle is also acute.

Terms to remember Vertex Plural: Vertices

More terms adjacent sides side opposite  C

Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180°. m  A + m  B + m  C = 180°

Term congruent figures – Two geometric figures that have exactly the same size and shape. All pairs of corresponding angles and sides are congruent. symbol: 

Example 1  A   F,  C   D,  B   E AB  FE, BC  ED, CA  DF ∆ABC  ∆ FED Identify all pairs of congruent corresponding parts and write a congruence statement

Example 3 Find the value of x. (2x+30)° m  M = 180º - 55º - 65 º m  M = 60 º m  M = m  T 60 = 2x + 30 x = 15

Try This! Find the value of x. (4x+15)°

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.

Example 1 StatementsReasons

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.

Example 2 Prove: ∆AEB  ∆CED StatementsReasons

Angle-Side-Angle (ASA) Congruence Postulate 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 two triangles are congruent. If  A   D, AC  DF, and  C   F, then  ABC   DEF

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. If  A   D,  C   F, and BC  EF, then  ABC   DEF

Hypotenuse-Leg (HL) Congruence Theorem 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.

Example 2 Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Yes! AASNo!

Try This! Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use. Yes! ASA No! AAA is NOT a congruence postulate or theorem

Homework Page 238 numbers 1-3, 13,14 Page 244 numbers 2, 4, 10, 12, 14, 15 Page 251 Numbers 2-14 Evens