1.
How can you prove these triangles are congruent
Correct Answer
B. SAS
Explanation
SAS stands for Side-Angle-Side congruence criterion. It states that if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the triangles are congruent. In this case, the given triangles can be proven congruent using SAS if we have two sides of one triangle congruent to the corresponding sides of another triangle, and the included angle between those sides is also congruent.
2.
Correct Answer
D. D
3.
How can you prove the triangles are congruent?
Correct Answer
B. SAS
Explanation
The answer is SAS, which stands for Side-Angle-Side. This means that if two triangles have two sides and the included angle of one triangle congruent to the corresponding two sides and included angle of the other triangle, then the triangles are congruent. This can be proven by showing that the corresponding sides and angles are equal in both triangles.
4.
How can you prove the triangles are congruent?
Correct Answer
A. SAS
Explanation
SAS stands for Side-Angle-Side, which is a congruence postulate in geometry. It states that if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the triangles are congruent. Therefore, if you can prove that two triangles have two sides that are congruent and the included angle between them is congruent, you can conclude that the triangles are congruent.
5.
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.
6.
Refer to the figure. Complete the congruence statement
Correct Answer
C. Triangle VUT
Explanation
The congruence statement can be completed as "Triangle VUT is congruent to Triangle TUV" because the order of the vertices in the congruence statement does not matter. In other words, the triangles are congruent regardless of the order in which the vertices are listed.
7.
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, they must be the same size and shape, making them congruent.
8.
by the _______________.
Correct Answer
C. SSS Postulate
Explanation
The SSS Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. This means that if all three sides of a triangle are equal in length to the corresponding sides of another triangle, then the two triangles are congruent. Therefore, the correct answer is the SSS Postulate.
9.
Correct Answer
A. SAS Postulate
10.
Which postulate or theorem shows that
Correct Answer
D. AAS Theorem
Explanation
The AAS (Angle-Angle-Side) theorem states that if two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent. This theorem can be used to prove that two triangles are congruent by showing that their corresponding angles and sides are congruent.
11.
By which reason can it be proven that triangles DAB and DAC are congruent?
Correct Answer
B. AAS
Explanation
The reason that triangles DAB and DAC can be proven congruent is by 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, we know that angle D is congruent to itself, angle A is congruent to angle A, and side AD is congruent to itself. Therefore, by the AAS criterion, triangles DAB and DAC are congruent.
12.
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.
13.
How can you prove the 2 triangles are congruent?
Correct Answer
D. SSS
Explanation
The answer is SSS, which stands for Side-Side-Side. This means that if all three sides of one triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent. In other words, if the lengths of all three sides of two triangles are equal, then the triangles are congruent.