Lesson 4.1 To 4.3 Quiz

Explanation
A scalene triangle is a triangle that has three sides of different lengths. Since congruent sides are sides that have the same length, a scalene triangle does not have any congruent sides. Therefore, the correct answer is 0.

Explanation
In an equiangular triangle, all three angles are congruent, meaning they have the same measure. Therefore, the correct answer is 3, as there are three congruent angles in an equiangular triangle.

Explanation
The missing angle can be determined by subtracting the given angles from 180 degrees, since the sum of the angles in a triangle is always 180 degrees. Therefore, 180 - 133 - 43 = 4. Since the missing angle is less than 180 degrees, it must be positive. Thus, the missing angle is 47 degrees.

Explanation
If triangle ABC is congruent to triangle JLK, it means that they have the same shape and size. Therefore, the corresponding sides of these triangles are congruent. Since AB is a side of triangle ABC, the corresponding side in triangle JLK that is congruent to AB is JL.

Explanation
In a congruent triangle, corresponding angles are equal. Since triangle ABC is congruent to triangle FGH, angle B in triangle ABC is congruent to angle G in triangle FGH.

Explanation
If triangle DEF is congruent to triangle XYZ, it means that they have the same shape and size. Therefore, corresponding sides of the triangles are equal. Given that DE = 14, it implies that XY, which corresponds to DE, is also equal to 14.

Explanation
The congruence postulate that can be used to prove that the two triangles are congruent is SAS (Side-Angle-Side). 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, the given information is that one side and the two angles of one triangle are congruent to one side and the two angles of another triangle, satisfying the conditions of the SAS postulate. Therefore, the triangles can be proven to be congruent using the SAS postulate.

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

Explanation
The triangle can be classified as a right triangle because it has one angle that measures 90 degrees. It can also be classified as an isosceles triangle because it has two sides that are equal in length.

Explanation
Two triangles with the same side lengths are always congruent. This is because the side lengths determine the shape and size of a triangle. If two triangles have the same side lengths, then all corresponding angles will also be equal, making them congruent. Therefore, the statement that two triangles with the same side lengths 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.