Section 8-1 Proving Triangles Congruent: SSS and SAS
Postulate 8-1 side side side (SSS): If three sides of
one triangle are congruent to three sides of another
triangle then the two triangles are congruent
Included angles- angle created by 2 segments which are sides
Included segments- one segment shared by two angles
Postulate 8-2 side angle sude (SAS): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent
Section8-2
Proving Triangles Using ASA and AAS
Postulate 8-3 Angle Side Angle (ASA):
If two angles and the included side of the triangle are congruent to two angles and the included side of
another triangle, then the two triangles are congruent
Theorem 8-1 Angle Angle side (AAS):
Ff two triangles and a non included side of the corresponding non included side of another triangle, then the triangles are congruent
Section 8-3
Congruent Right Triangles
Theorem 8-2 Hypotenuse Leg (HL):
If the hypotenuseand leg of one right triangle are congruent to the hypotneuse and leg of another right triangle, then the triangles are congruent
3 Conditions to use HL
1. Have to have 2 right triangles or <'s
2. A pair of congruent hypotenuses
3. a pair of congruent legs
Section 8-4
CPCTC Corresponding Parts of Congruent Triangles are congruent
Section 8-5
Overlapping Triangles
Look For Congruent Parts
Common parts- In both triangles, a piece thats over lapping
Common angle- In both triangles, an angle that's shared
Common segment- In both triangles, a segment that's shared
Section 8-1 Proving Triangles Congruent:
SSS and SAS
Postulate 8-1 Side Side Side (SSS): If three sides of one triangle are congruent to three sides of another triangle then the two triangles are congruent
Included Angles- Angle created by 2 segemtns which are sides
Included segments- One segment shared by two angles
Postulate 8-2 Side Angle Sude (SAS): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent
Section 8-2
Proving Triangles Using ASA and AAS
Postulate 8-3 Angle Side angle (ASA): If two angles and the included side of the triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent
Theorem 8-1 Angle Angle Side (AAS):
If two triangles and a non included side of the corresponding non included side of another triangle, then the triangles are congruent
Section 8-3
Congruent Right Rriangles
Theorem 8-2 Hypotenuse Leg (HL):
If the hypotenuse and a leg of one right triangle are congruent to the hypotneuse and leg of another right triangle, then the triangles are congruent
3 Conditions to Use HL
1. Have to have 2 right triangles or <'s
2. A pair of congruent hypotenuses
3. A pair of congruent legs
Section 8-4
CPCTC corresponding parts of congruent triangles are congruent
Section 8-5
Overlapping Triangles
Look for congruent parts
Common parts-in both triangles, a piece thats over lapping
Common angle-in both triangles, an angle that's shared
common segment- in both triangles, a segment that's shared
Section 8-1
Proving triangles congruent: SSS and SAS
Postulate 8-1 side side side (SSS): If three sides of one triangle are congruent to three sides of another triangle then the two triangles are congruent
Included angles-angle created by 2 segemtns which are sides included segments- one segment shared by two angles
Postulate 8-2 side angle sude (SAS): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent
Section 8-2
Proving Triangles Using ASA and AAS
Postulate 8-3 angle side angle (ASA): If two angles and the included side of the triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent
Theorem 8-1 angle angle side (AAS): If two triangles and a non included side of the corresponding non included side of another triangle, then the triangles are congruent
Section 8-3
Congruent Right Triangles
Theorem 8-2 hypotenuse leg (HL): If the hypotenuse and a leg of one right triangle are congruent to the hypotneuse and leg of another right triangle, then the triangles are congruent
3 Conditions to Use HL
1. Have to have 2 right triangles or <'s
2. A pair of congruent hypotenuses
3. A pair of congruent legs
Section 8-4
CPCTC corresponding parts of congruent triangles are congruent
Section 8-5
Overlapping Triangles
Look for Congruent Parts
Common parts- in both triangles, a piece thats over lapping
Common angle- in both triangles, an angle that's shared
Common segment- in both triangles, a segment that's shared
Section 8-1 proving triangles congruent:
SSS and SAS
Postulate 8-1 side side side (SSS):
If three sides of one triangle are congruent to three sides of another triangle then the two triangles are congruent
Included angles- angle created by 2 segemtns which are sides
Included segments- one segment shared by two angles
Postulate 8-2 side angle sude (SAS): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent
Section 8-2
proving triangles using ASA and AAS
Postulate 8-3 angle side angle (ASA): If two angles and the included side of the triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent
Theorem 8-1 angle angle side (AAS): If two triangles and a non included side of the corresponding non included side of another triangle, then the triangles are congruent
Section 8-3
Congruent Right Triangles
Theorem 8-2 hypotenuse leg (HL): If the hypotenuse and a leg of one right triangle are congruent to the hypotneuse and leg of another right triangle, then the triangles are congruent
3 conditions to use HL
1. Have to have 2 right triangles or <'s
2. A pair of congruent hypotenuses
3. A pair of congruent legs
Section 8-4
CPCTC corresponding parts of congruent triangles are congruent
Section 8-5
Overlapping Triangles
Look for Congruent Parts
Common parts- in both triangles, a piece thats over lapping
Common angle- in both triangles, an angle that's shared
Common segment- in both triangles, a segment that's shared
Postulate 8-1 side side side (SSS):
If three sides of one triangle are congruent to three sides of another triangle then the two triangles are congruent
Included angles- angle created by 2 segemtns which are sides included segments- one segment shared by two angles
Postulate 8-2 side angle sude (SAS):
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent
Section 8-2
Proving Triangles Using ASA and AAS
Postulate 8-3 Angle Side Angle (ASA): If two angles and the included side of the triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent
Theorem 8-1 angle angle side (AAS): If two triangles and a non included side of the corresponding non included side of another triangle, then the triangles are congruent
Section 8-3
Congruent Right Triangles
Theorem 8-2 hypotenuse leg (HL): if the hypotenuse and a leg of one right triangle are congruent to the hypotneuse and leg of another right triangle, then the triangles are congruent
3 Conditions to Use HL
1. Have to have 2 right triangles or <'s
2. A pair of congruent hypotenuses
3. A pair of congruent legs
Section 8-4
CPCTC corresponding parts of congruent triangles are congruent
Section 8-5
Overlapping Triangles
Look for Congruent Parts
Common parts- in both triangles, a piece thats over lapping
Common angle- in both triangles, an angle that's shared
Common segment- in both triangles, a segment that's shared
