Chapter 4 BJ BROWN Identify and Classify Triangles by Angles and Sides Acute Triangle- all angles are acute
Obtuse Triangle- one angle is obtuse
Right Triangle- one right angle
Scalene Triangle- no congruent sides
Isosceles Triangle- at least 2 congruent sides
Equilateral Triangle- all sides congruent
Proving Right Triangles are Congruent Hypotenuse-Angle Theorem (HA) A
B
2
C 1
D
E
Leg-Leg Theorem (LL) A
B
D C
E
Leg-Angle Theorem (LA) B
A
1
2
C
D
Hypotenuse-Leg Theorem (HL) A
C
D
B
E
Proving Triangles Are Congruent by SSS (Side-Side-Side Postulate) and SAS (Side-Angle-Side Postulate) Side-Side-Side (SSS) –if 3 sides of a triangle are congruent to 3 sides of another triangle then the triangles are congruent R
S
Q
T
Side-Angle-Side (SAS) –if 2 sides of a triangle are congruent to the corresponding sides of another triangle and its included sides then the triangles are congruent R
S
1
2 Q T
Proving Triangles Are Congruent by AAS (Angle-Angle-Side Postulate) and ASA (Angle-Side-Angle Postulate) Angle-Side-Angle (ASA) – if 2 angles of a triangle and their included side are congruent to 2 angles and the included side of another triangle then the triangles are congruent A
E 3
5
1 B 2
6
4
D
C
Angle-Angle-Side (AAS) - if 2 angles and their non-included side are congruent to 2 angles and their non-included side of another triangle then the triangles are congruent A
E 1
2
B
3 D
4 C