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6.1A. Triangle Congruence Postulates T.2.G.1 Apply congruence (SSS …) and similarity (AA …) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification LG.1.G.6 Give justification for conclusions reached by deductive reasoning.

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slide1

6.1A

Triangle Congruence Postulates

T.2.G.1 Apply congruence (SSS …) and similarity (AA …) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification

LG.1.G.6 Give justification for conclusions reached by deductive reasoning

vocabulary
Vocabulary
  • Reflexive property: For every number a, a = a
  • Transitive property: If a = b and b = c, then a = c
  • Similarity: Two shapes are similar if corresponding angles are congruent and corresponding sides are proportional
  • Congruency: Two shapes are congruent if corresponding angles and sides are congruent

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triangle congruence postulates
Triangle Congruence Postulates

SIDE-SIDE-SIDE (SSS)

Two triangles are congruent if all corresponding sides are congruent.

A

D

E

F

B

C

triangle congruence postulates1
Triangle Congruence Postulates

ANGLE-SIDE-ANGLE (ASA)

Two triangles are congruent if two adjacent angles and their included side are congruent.

B

R

A

T

E

M

triangle congruence postulates2
Triangle Congruence Postulates

ANGLE-ANGLE-SIDE (AAS or SAA)

Two triangles are congruent if two adjacent angles and a non-included side are congruent.

C

D

T

G

A

O

triangle congruence postulates3
Triangle Congruence Postulates

SIDE-ANGLE-SIDE (SAS)

Two triangles are congruent if two adjacent sides and an included angle are congruent

B

G

L

Y

R

O

not congruence postulates
NOT Congruence Postulates

ANGLE-ANGLE-ANGLE (AAA)

If all three angles on each triangle are congruent to each other, then the triangles are similar, but not congruent.

not congruence postulates1
NOT Congruence Postulates

ANGLE-SIDE-SIDE (Bad word postulate)

special case of the bad word postulate
Special Case of the Bad Word Postulate

HYPOTENUSE-LEG (HL)

Tworight triangles are congruent if their hypotenuses and one pair of corresponding legs are congruent.

S

D

M

L

P

R

identifying congruence postulates
Identifying Congruence Postulates

What congruence postulate is being demonstrated here?

SAA (or AAS)

cpctc
CPCTC

Corresponding parts of congruent triangles are congruent.

Once we have determined that two triangles are congruent, we know that all of their corresponding parts are congruent.

B

R

A

T

E

M

example
Example

Determine whether the following triangles can be proven congruent using the given information. If congruency can be proven, write a congruence statement and identify the postulate used to prove congruency. If not enough information is given, write not possible.

example1

A

C

B

T

S

Example

Determine whether the following triangles can be proven congruent using the given information. If congruency can be proven, write a congruence statement and identify the postulate used to prove congruency. If not enough information is given, write not possible.

example2

A

B

C

D

Example

Determine whether the following triangles can be proven congruent using the given information. If congruency can be proven, write a congruence statement and identify the postulate used to prove congruency. If not enough information is given, write not possible.

example3

B

D

A

C

E

Example

Determine whether the following triangles can be proven congruent using the given information. If congruency can be proven, write a congruence statement and identify the postulate used to prove congruency. If not enough information is given, write not possible.

now you try
Now You Try…

Determine whether the following triangles can be proven congruent using the given information. If congruency can be proven, write a congruence statement and identify the postulate used to prove congruency. If not enough information is given, write not possible.

C

D

B

A

example4
Example

The following triangles are congruent. State one additional fact and the congruence postulate it would complete.

A

C

B

D

E

example5

W

R

S

V

T

U

Example

The following triangles are congruent. State one additional fact and the congruence postulate it would complete.