1.
Which combination of congruent corresponding parts can you not use to prove two triangles congruent?
Correct Answer
B. AAA
Explanation
You remembered that you must have at least one pair of congruent sides.
2.
Refer to the figure. Complete the congruence statement
Correct Answer
C. Triangle VUT
Explanation
The correct answer is Triangle VUT because the vertices of the triangles are listed in a clockwise order. In congruence statements, the order of the vertices matters, and the given answer follows the correct order.
3.
Two triangles are necessarily congruent if and only if __________.
Correct Answer
C. Their corresponding sides and corresponding angles are congruent.
Explanation
Two triangles are necessarily congruent if and only if their corresponding sides and corresponding angles are congruent. This is because congruent triangles have the same shape and size. The corresponding sides of congruent triangles are equal in length, and the corresponding angles are equal in measure. Therefore, if both the sides and angles of two triangles are congruent, then the triangles are necessarily congruent.
4.
by the _______________.
Correct Answer
C. SSS Postulate
Explanation
The SSS (Side-Side-Side) Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. In other words, if all three sides of one triangle have the same length as the corresponding three sides of another triangle, then the two triangles are congruent. This postulate is used to determine congruence between triangles based solely on the lengths of their sides.
5.
Correct Answer
A. SAS Postulate
6.
Which postulate or theorem shows that
Correct Answer
D. AAS Theorem
Explanation
The AAS (Angle-Angle-Side) theorem states that 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 two triangles are congruent. This theorem is used to prove congruence between triangles when the given information involves two angles and a non-included side.
7.
ΔSAM≅ΔRATWhich statement is NOT necessarily true?
Correct Answer
C.
Explanation
The statement "MA = TA" is not necessarily true. While it is given that ΔSAM is congruent to ΔRAT, it does not guarantee that the corresponding angles and sides are equal. Therefore, it is not necessary for the measure of angle MA to be equal to the measure of angle TA.
8.
By which reason can it be proven that triangles DAB and DAC are congruent?
Correct Answer
B. AAS
Explanation
The reason why triangles DAB and DAC can be proven congruent is by using the AAS (Angle-Angle-Side) congruence criterion. This criterion 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. In this case, the two angles (AAA) are congruent, and the included side (side AD) is congruent. Therefore, by the AAS criterion, triangles DAB and DAC are congruent.
9.
Use the triangle inequality to determine the smallest angle in the figure.∠SCI
Correct Answer
B.
Explanation
∠CIS. This angle is opposite from the smallest side. Therefore, according to the triangle inequality, it is the smallest angle.
10.
Which pair of triangles would you use ASA to prove the congruence of the 2 triangles?
Correct Answer
B. B
Explanation
The triangles shown in choice C can be proven congruent by ASA. The triangles have 2 pairs of congruent angles and pair of congruent included sides.
11.
List the sides of the triangle in order from SHORTEST to LONGEST.
Explanation
The sides of the triangle in order from shortest to longest are BA, BC, and AC.
12.
The shortest side of ΔDEF is ___________.
Explanation
The shortest side of triangle ΔDEF is DE.