Triangle Congruence Theorems
What is the name of the theorem that states that if two angles and the included side of one triangle are congruent to the corresponding angles and included side of another triangle, then the triangles are congruent?
ASA
What are the three properties of congruence for triangles?
The three properties of congruence for triangles are: angle congruence, side congruence, and CPCTC.
If two triangles are congruent, what can you conclude about their corresponding angles?
The corresponding angles of congruent triangles are congruent.
What does the term "congruent triangles" mean?
Congruent triangles have the same shape and size, with corresponding sides and angles that are equal.
What does the SSS Congruence state?
The Side-Side-Side (SSS) Congruence states that if the three sides of one triangle are congruent to the corresponding sides of another triangle, then the two triangles are congruent.
Which triangle congruence theorem states that if all three sides of one triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent?
SSS
How many sides of a triangle need to be congruent to establish triangle congruence using the SAS property?
Two sides of a triangle need to be congruent to establish triangle congruence using the SAS property.
If two triangles are congruent, what can you conclude about their corresponding sides?
The corresponding sides of congruent triangles are congruent.
Name the four methods of proving triangle congruence.
SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side) are the four methods of proving triangle congruence
True or False: If two triangles have their corresponding sides equal, they are not necessarily congruent.
True. Having equal corresponding sides is necessary but not sufficient for proving triangle congruence. Other conditions, such as congruent angles, need to be considered.
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, which triangle congruence theorem can be used to prove the triangles congruent?
SAS
How many angles of a triangle need to be congruent to establish triangle congruence using the ASA property?
Two angles of a triangle need to be congruent to establish triangle congruence using the ASA property.
Name two postulates or theorems for proving triangle congruence.
SAS (Side-Angle-Side), ASA (Angle-Side-Angle), SSS (Side-Side-Side), AAS (Angle-Angle-Side).
Define the term "corresponding parts" in the context of triangle congruence.
Corresponding parts refer to the matching sides and angles of congruent triangles.
If triangle ABC is congruent to triangle DEF by the SSS Congruence, what can you conclude about their corresponding angles?
The corresponding angles of congruent triangles will also be equal.
What is the name of the theorem that states if two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent?
AAS
If all three sides and all three angles of two triangles are congruent, what can we conclude about the triangles?
If all three sides and all three angles of two triangles are congruent, the triangles are congruent.
State the CPCTC (Corresponding Parts of Congruent Triangles are Congruent) theorem.
If two triangles are congruent, then their corresponding parts (angles and sides) are congruent.
Or basically if if triangles are the same both triangles will have same length and sides and angles.
In triangle congruence, what are vertically opposite angles?
Vertically opposite angles are the angles formed by the intersection of two lines and are opposite each other. They have equal measures.
Can two triangles with the same side lengths but different angle measures be congruent?
No. Congruent triangles must have both corresponding sides and angles equal.
Which triangle congruence theorem states that if two angles and the included side of one triangle are congruent to the corresponding angles and included side of another triangle, then the triangles are congruent?
ASA
If two triangles have two pairs of corresponding congruent angles, what can we conclude about the triangles?
If two triangles have two pairs of corresponding congruent angles, the triangles are similar but not necessarily congruent.
True or False: ASA (Angle-Side-Angle) congruence theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
True
Explain what the Hypotenuse-Leg (HL) Congruence Theorem states.
The Hypotenuse-Leg (HL) Congruence Theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
Provide an example of two congruent triangles using the SSS Congruence.
Two triangles with side lengths 3 cm, 4 cm, and 5 cm would be an example of congruent triangles using the SSS Congruence.