Triangle congruence occurs when two triangles have the same shape and size, meaning all corresponding sides and angles are equal.
Name one sign of triangle congruence.
One sign of triangle congruence is Side-Side-Side (SSS).
Explain the Side-Side-Side (SSS) congruence rule.
If all three sides of one triangle are equal to all three sides of another triangle, the triangles are congruent.
What is the Side-Angle-Side (SAS) rule for triangle congruence?
If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
What does the Angle-Side-Angle (ASA) rule state?
The ASA rule states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
Describe the Angle-Angle-Side (AAS) congruence rule.
If two angles and a non-included side of one triangle are equal to two angles and a corresponding non-included side of another triangle, the triangles are congruent.
How is the Hypotenuse-Leg rule used in right triangles?
The Hypotenuse-Leg (HL) rule states that in right triangles, if the hypotenuse and one leg are equal, the triangles are congruent.
In the SAS rule, what is meant by the included angle?
The included angle is the angle formed between the two sides being compared in two triangles.
Which triangle congruence rule requires knowing all three sides?
The Side-Side-Side (SSS) rule requires knowing all three sides.
Can triangles be congruent if only two angles are equal?
No, the triangles must also have at least one corresponding side equal, such as in the ASA or AAS rules.
What is necessary for triangles to be congruent using the AAS rule?
Two angles and any one corresponding side must be equal for AAS congruence.
Is it possible for two triangles to be congruent if one is smaller than the other?
No, congruent triangles must be exactly the same size and shape.
Why can't the SSA rule be used to prove triangle congruence?
SSA cannot prove congruence because it can result in two different triangles, as the included angle is not known.
What is necessary for the Hypotenuse-Leg theorem to be applied?
The triangles must be right triangles, and their hypotenuses and one leg must be equal.
Give an example where the ASA rule is applicable.
If one triangle has angles of 40° and 60° with an included side of 5cm, and another triangle has the same angles and side, they are congruent using ASA.