#1
Which congruence postulate or theorem is applicable when all three sides of one triangle are congruent to all three sides of another triangle?
Side-Side-Side (SSS)
ExplanationCongruence is proven when all three sides of one triangle are equal to the corresponding sides of another triangle.
#2
Which congruence postulate or theorem is applicable when all three angles of one triangle are congruent to all three angles of another triangle?
Angle-Angle-Angle (AAA)
ExplanationCongruence is proven when all three angles of one triangle are equal to the corresponding angles of another triangle.
#3
Which postulate 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 triangles are congruent?
Angle-Angle-Side (AAS)
ExplanationCongruence is established when two angles and the included side of one triangle match those of another triangle.
#4
In triangle congruence, if two corresponding angles and the included side of one triangle are congruent to two corresponding angles and the included side of another triangle, what postulate can be used to prove congruence?
Angle-Side-Angle (ASA)
ExplanationCongruence is proven when two corresponding angles and the included side of one triangle are equal to those of another triangle.
#5
If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, what postulate can be used to prove congruence?
Side-Angle-Side (SAS)
ExplanationCongruence is established when two angles and a non-included side of one triangle match those of another triangle.
#6
If two angles and a side that is not between them (non-included side) of one triangle are congruent to two angles and a side that is not between them (non-included side) of another triangle, what postulate can be used to prove congruence?
Angle-Angle-Side (AAS)
ExplanationCongruence is established when two angles and a non-included side of one triangle match those of another triangle.
#7
Which of the following is NOT a condition for proving triangle congruence using the SSS postulate?
The triangles are similar.
ExplanationTriangle congruence is not dependent on the triangles being similar when using the Side-Side-Side (SSS) postulate.
#8
What is the condition for proving triangle congruence using the SAS postulate?
Two pairs of corresponding sides and the included angle are equal.
ExplanationTriangle congruence is established when two pairs of corresponding sides and the included angle are equal using the Side-Angle-Side (SAS) postulate.
#9
What does the Side-Side-Angle (SSA) condition state in terms of triangle congruence?
If two pairs of corresponding sides and a non-included angle are congruent, the triangles are congruent.
ExplanationTriangle congruence is established when two pairs of corresponding sides and a non-included angle are equal using the Side-Side-Angle (SSA) condition.
#10
Which of the following conditions is required to prove triangle congruence using the ASA postulate?
Two pairs of corresponding sides and a non-included angle are congruent.
ExplanationTriangle congruence is established when two pairs of corresponding sides and a non-included angle are equal using the Angle-Side-Angle (ASA) postulate.