Classifying And Finding Missing Angles

Explanation
In a scalene triangle, all three sides have different lengths, so none of the sides are congruent. Therefore, the correct answer is 0.

Explanation
An equiangular triangle is a triangle in which all three angles are congruent. Since all three angles in an equiangular triangle are congruent, the correct answer is 3.

Explanation
The missing angle can be determined by subtracting the given angles from 180 degrees, which is the sum of the angles in a triangle. Therefore, 180 - 133 - 43 = 4 7.

Explanation
If triangle ABC is congruent to triangle JLK, it means that they have the same shape and size. In congruent triangles, corresponding sides are equal in length. Therefore, if AB is a side of triangle ABC, the corresponding side in triangle JLK that is congruent to AB would be JL.

Explanation
In the given triangle, triangle ABC is congruent to triangle FGH. This means that the corresponding angles of the two triangles are equal. Since angle B is a corresponding angle to angle G, it is congruent to angle G.

Explanation
If triangle DEF is congruent to triangle XYZ, it means that they have the same shape and size. Since DE = 14, DF = 15, and EF = 9, we can conclude that the corresponding sides of triangle XYZ are also 14, 15, and 9. Therefore, the length of XY is 14.

Explanation
The SSS (Side-Side-Side) congruence postulate can be used to prove that the two triangles are congruent. According to this postulate, if the three sides of one triangle are congruent to the corresponding three sides of another triangle, then the two triangles are congruent. In other words, if all three pairs of corresponding sides are equal in length, then the triangles are congruent.

Explanation
The SAS (Side-Angle-Side) congruence postulate can be used to prove that the two triangles are congruent. This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In this case, if we have two triangles with one pair of corresponding sides congruent, another pair of corresponding sides congruent, and the included angles congruent, we can use the SAS congruence postulate to prove their congruence.

Explanation
The AAS (Angle-Angle-Side) congruence postulate can be used to prove that the two triangles are congruent. This postulate 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. In this case, we have two angles that are congruent and a side that is not included between those angles that is also congruent, which satisfies the conditions of the AAS postulate. Therefore, we can conclude that the two triangles are congruent.

Explanation
The ASA (Angle-Side-Angle) congruence postulate can be used to prove that the two triangles are congruent. According to this postulate, 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. In this case, we can use ASA to show that the two triangles have two congruent angles (A and A) and a congruent side (the side between the two angles). Therefore, the triangles are congruent.

Explanation
This triangle can be classified as scalene because all three sides have different lengths. It can also be classified as acute because all three angles are less than 90 degrees.

Explanation
The triangle can be classified as a right triangle because it has one angle measuring 90 degrees. Additionally, it can also be classified as an isosceles triangle because it has two sides of equal length.

Explanation
Two triangles with the same side lengths are always congruent. In order for two triangles to be congruent, all corresponding sides and angles must be equal. Therefore, if two triangles have the same side lengths, they must also have the same angles, making them congruent. Hence, the statement "You can build two triangles that have the same side lengths but are not congruent" is false.

Explanation
An isosceles triangle has AT LEAST two congruent sides. An equilateral triangle has three congruent sides, which means that it has at least two sides congruent.